Decentralization using Quantum Blockchain: A Theoretical Analysis

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identifier 10.1109/TQE.2020.Doi Number

Decentralization using Quantum Blockchain: A

Theoretical Analysis

Zebo Yang

, Student Member, IEEE, Tara Salman

, Member, IEEE, Raj Jain

, Life Fellow,

IEEE, and Roberto Di Pietro

, Fellow, IEEE

Department of Computer Science and Engineering, Washington University, St. Louis, MO 63130 USA

Department of Computer Science, Texas Tech University, Lubbock, TX 79409-3104 USA

College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

Corresponding author: Zebo Yang (email: [email protected]).

This publication was made possible by the NPRP grant # NPRP11S-0109-180242 from the Qatar National Research Fund (a member of The Qatar Foundation.

The findings achieved herein are solely the responsibility of the authors.

ABSTRACT Blockchain technology has been prominent recently due to its applications in cryptocurrency.

Numerous decentralized blockchain applications have been possible due to blockchains’ nature of distributed,

secured, and peer-to-peer storage. One of its technical pillars is using public-key cryptography and hash

functions, which promise a secure, pseudo-anonymous, distributed storage with non-repudiation. This

security is believed to be difficult to break with classical computational powers. However, recent advances

in quantum computing have raised the possibility of breaking these algorithms with quantum computers, thus,

threatening the blockchains’ security. Quantum-resistant blockchains are being proposed as alternatives to

resolve this issue. Some propose to replace traditional cryptography with post-quantum cryptography—others

base their approaches on quantum computer networks or quantum internets. Nonetheless, a new security

infrastructure (e.g., access control/authentication) must be established before any of these could happen. This

article provides a theoretical analysis of the quantum blockchain technologies that could be used for

decentralized identity authentication. We put together a conceptual design for a quantum blockchain identity

framework (QBIF) and give a review of the technical evidence. We investigate its essential components and

feasibility, effectiveness, and limitations. Even though it currently has various limitations and challenges, we

believe a decentralized perspective of quantum applications is noteworthy and likely.

INDEX TERMS Blockchains, Consensus protocol, Decentralized applications, Identity management

systems, Quantum computing, Quantum networks.

INTRODUCTION

Blockchain technology, as a peer-to-peer technique that

keeps track of sequential data, and its numerous applications,

e.g., cryptocurrencies, has attracted massive attention in

recent years. Besides cryptocurrencies, it provides an

innovative way to realize decentralized applications, which

has led to many interesting research topics, such as

decentralized consensus mechanisms, trustless security,

cryptographical access controls, and non-repudiation [1].

Blockchain applications span various sectors, including

finance, healthcare, the Internet of Things, cybersecurity,

and many others [2, 3].

Public key cryptography and hash functions are one of the

blockchains’ main pillars to realize secure access control and

distributed data. Public key cryptography schemes generally

use two keys for encryption/decryption, user authentication,

and digital signatures for secure data transmissions. These

schemes require public and private key pairs that can be self-

generated or obtained from a public key infrastructure (PKI)

consisting of a hierarchy of certificate authorities. In

blockchains, they are used to authenticate network nodes. For

example, Bitcoin [4] and most other existing blockchain

platforms use the public-key method for elliptic curve

cryptography-based digital signature algorithm (ECDSA) for

user authentication and access control. Also, hash functions

are used to securely “chain” the data stored in blocks by

referencing each block to its previous/parent block using the

previous block’s hash. For example, SHA-256 is used as a

hash function to chain the data blocks in Bitcoin.

Public key cryptography and hash functions are prevalently

used and are secure enough against factorization attacks and

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 2

brute force attacks using classical computers. This is due to the

difficulty of solving large-number factorization and reversing

one-way functions. However, quantum computers have

provided polynomial-time solutions to solve factorization

(e.g., Shor's algorithm) [5] and efficient ways to reverse one-

way hash functions in

(e.g., Grover’s algorithm) [6].

In addition, such algorithms can also be used to find hash

collisions efficiently, which could result in data tampering in

blockchains [7]. Recent studies have shown the significance

of tackling potential quantum threats to classical blockchains

[8, 9, 10].

To address the potential quantum threats, new classical

cryptography algorithms, called post-quantum cryptography,

are being developed [11]. They use cryptographic primitives

other than factorization, such as lattice, for public key schemes

to avoid potential threats based on Shor's algorithm.

Blockchains use public key schemes to secure their user

accounts (public keys to generate addresses and pass codes

based on private keys). If such public key schemes are

endangered (e.g., pass codes can be found), user assets (e.g.,

cryptocurrencies) will no longer be secure. Post-quantum

blockchains that use post-quantum public key cryptography

have been developed and are claimed to be immune to

quantum attacks [12]. They replace blockchains' current

public key cryptography with post-quantum counterparts. On

the other hand, the vulnerability of hash functions is not as

impactful since we can increase the hash length to resist

quantum attacks (e.g., a hash collision that maps two inputs to

the same hash value). However, increasing the length

sacrifices performance.

Moreover, quantum blockchains that are solely (or in a

hybrid manner) based on quantum computer networks (or the

so-called quantum Internet) are also being explored [13, 14,

15, 16, 17]. The classical data chain has been re-designed in a

quantum manner by correlating quantum states over

entanglements. “Unconditional security” of quantum

decentralization is claimed for such quantum blockchains [16,

17].

However, quantum blockchains are still in their early phase

and thus still lack sufficient research and implementation on

the infrastructures. Quantum blockchain infrastructures such

as access control and user authentication must be established

before any quantum decentralization. Hence, in this article, we

theoretically explore the essential components of a

decentralized quantum application based on quantum

blockchains.

The contributions of this article are listed below:

• We provide a theoretical analysis of quantum

blockchains and their use for a decentralized identity

authentication application.

• We accommodate the classical blockchain identity

management with quantum advantages against the

quantum threats (to classical cryptography).

• We put together a conceptual design for a quantum

blockchain identity framework (QBIF) and give a

review of the related technologies.

• We investigate the feasibility, effectiveness, and

limitations of QBIF’s essential components.

Even though it comes with various limitations and

challenges, we believe a decentralized perspective of quantum

applications is noteworthy and likely. Identity management

frameworks promise to maintain users’ identity information

securely, and decentralized identity removes the concerns of

centralization that violates user privacy [18]. Layering it to the

quantum domain gets rid of the quantum threats. We believe

that making blockchain quantum native and rebuilding

everything from there would be an ideal way to implement

quantum blockchains and their applications, but the current

quantum technologies do not allow us to do that. This paper

analyzes the classical-to-quantum transition from a more

realistic perspective by adopting existing technologies.

The rest of the paper is organized as follows. Section II

discusses the current technologies of quantum blockchains

and blockchain-based identity. Then, in Section III, we give a

pedagogical introduction to the quantum technologies that

QBIF is layered on. With these two sections giving

background and preliminary knowledge, in Section IV, we

introduce the conceptual design of QBIF module by module.

After that, in Section V, we discuss the challenges and

limitations of QBIF. Finally, we give overall conclusions in

Section VI.

II. BACKGROUND AND RELATED WORK

In this section, we introduce blockchains, quantum

blockchains, and blockchain-based identity applications.

BLOCKCHAINS AND QUANTUM BLOCKCHAINS

A blockchain is a shared and immutable ledger that maintains

data in the form of transactions [4]. Transactions are linked by

a Merkle tree and stored in blocks chained by hash functions.

A blockchain is composed of a peer-to-peer distributed

network where each node keeps a copy of a growing chain of

blocks, and the network uses a consensus protocol to add new

blocks and agree on the sequence of these blocks.

In general, blockchain users’ (or clients’) broadcasting of

transactions starts a blockchain process. A new block with the

latest transactions is made according to a particular consensus

protocol (e.g., Proof-of-Work, Proof-of-Stake) [1, 2]. Several

network nodes may compete to produce the new block for

incentives in these consensus protocols. For example, in

Bitcoin, the creator (called “miner”) of a block that is

eventually accepted as a permanent part of the chain wins the

competition and is rewarded. Each new block points to a

previously created block that the creator of the new block

accepts. Thus, a block followed by the longest chain in Bitcoin

is considered final. Other blockchains use other similar

methods for consensus.

This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 3

As discussed, every block has a hash value and points to its

previous hash value. If one of the blocks is tampered with, all

its following blocks become invalid. Blockchain nodes discard

this tampered copy of the chain and keep working on the chain

that the majority keeps. By adding extra data to block headers

or transactions, decentralized storage can be achieved.

Together with the blockchain event triggers, smart contracts

[19] and decentralized applications have been widely

developed.

User access control in blockchains relies on public-key

cryptography. Blockchain users keep their private keys as

passwords to their accounts and use their public keys as

account numbers. Transactions usually include their

generators’ (e.g., payers in cryptocurrency) signatures which

are done using their private keys. Network nodes that produce

blocks verify all the new transactions by validating the

signature with the generators’ public keys and discarding

invalid ones.

Commonly used public-key cryptography methods (e.g.,

ECDSA, RSA) rely on the difficulty of factoring large

numbers. It is easy to compute the product of two large

numbers, but it is challenging to factorize a large number. On

the other hand, the reliability of hash functions mainly depends

on the difficulty of reversing a one-way function, such as

SHA-256 and MD5. It is easy to compute the hash with inputs

but hard to invert given the hash. Every different input

generates a unique hash.

However, public-key cryptography and hash functions are

exposed due to the rapid development of quantum computers.

Shor's algorithm can factorize large numbers in a polynomial

time [5], endangering public key cryptography. Grover’s

algorithm [6] and its derivatives provide methods with a high

probability of finding the input to one-way functions by brute-

force searches (

, i.e., quadratic speedups) [17].

Post-quantum blockchains and quantum blockchains have

been proposed to solve these threats. Post-quantum

blockchains replace blockchains’ current cryptography with

classical post-quantum cryptography [12]. For example, post-

quantum cryptographies have been proposed to replace

ECDSA in blockchains (i.e., classical blockchains) with

quantum attack-resistant methods [16, 20, 21]. Quantum-

secured blockchains (i.e., hybrid blockchains) have been

designed on top of quantum key distribution (QKD) networks

[22, 23]. Quantum blockchains (i.e., fully quantum

blockchains) rebuild the classical blockchains in the domains

of quantum computing [13, 15, 16]. The notion of a quantum

blockchain is generally inspired by the non-separability of

quantum entanglement. The sensitivity of data tampering (i.e.,

tampering transaction history in a block) is much stronger in

quantum blockchains than in classical blockchains. Single

tampering of a block would cause the denial of the whole

chain, which indicates a higher level of security but a potential

denial of service on a blockchain node [13]. Note that, by

tampering, we mean tampering with the blockchain historical

data, not tampering with transmission information in general,

e.g., the man-in-the-middle attack. However, man-in-the-

middle attacks can happen in every aspect of a classical

network activity (at any communication link). For example, an

attack can be implemented during a key-generation

communication or any kind of communication that may leak a

secret key. If a key is leaked or intercepted, the blockchain

account associated with that key will be compromised. In the

quantum realm, such attacks will not be applicable (c.f., QKD

in Subsection II.C).

Furthermore, a hard fork in a blockchain is another

infamous issue. It sometimes happens due to disagreements in

the blockchain community (i.e., intentional hard fork). For

example, some want to upgrade the current blockchain (e.g.,

to increase the block size limit), but others disagree. Then, a

new version of the current blockchain appears and is kept by

users who believe in it (i.e., it becomes a hard fork). On the

other hand, a hard fork happening due to technical problems

(i.e., accidental hard fork) is rare because it will eventually be

resolved by the consensus mechanism (i.e., the majority

choosing the longer chain after some subsequent blocks being

produced). Hence, a typical consensus algorithm can address

it regardless of whether it is a quantum or classical blockchain.

BLOCKCHAIN-BASED IDENTITY APPLICATIONS

Decentralized identity management has been one of the most

prevalent applications of blockchains [24]. In the current

internet, we have imperfect systems for digital identities that

are kept in centralized storage. Centralized institutions or

companies must be trusted to maintain the authority of identity

authentication. Centralized identity violates user privacy and

might suffer from single-point-of-failure along with many

other centralization challenges. One data breach would cause

the leak of all confidential information. Also, user information

could be manipulated by the centralized entity for its own

interests.

Blockchain-based identity management has been proposed

to tackle the above issues [18, 25, 26, 27]. Every network node

has the same source of truth to follow in a blockchain-based

application. It replaces the centralized entity and provides

flexible identity authentication. Digital identities are created as

digital watermarks that are assigned to transactions. With a

smart contract, such identities could be used as authentication

methods for different purposes (e.g., financial and online

activities).

There are usually three roles in blockchain-based identity

management: owners, issuers, and verifiers. Issuers are trusted

parties (e.g., local governments and companies). They can

issue credentials (e.g., personal IDs and user profiles in an

application) for users (i.e., owners). Owners keep the

credentials to themselves and only provide them to third-party

entities (i.e., verifiers) to prove their statements (e.g., age,

ownership). Actual user credentials are not stored on

blockchains. Only user statements' attestations (i.e., proofs)

are kept on blockchains. For example, the proof of a user’s

date of birth may be stored on blockchains instead of the actual

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 4

date of birth. When the user provides the date of birth and the

proof, verifiers validate the issuer’s signature and decide the

genuineness of the user-provided data.

Blockchain-based identity applications have been prevalent

for years. For example, Bitnation [28], a blockchain-based

borderless voluntary nation project, has been developed to

reclaim the sovereignty of identity information and

governance services and has been working towards the vision

of world citizenship by registering identity information on the

global blockchain. ConsenSys [29] has provided decentralized

software services and applications. It has created a blockchain-

based identity system that maintains decentralized identifiers

for people, organizations, and objects on the blockchain

platform Ethereum [19]. Start-ups and big companies also

have proposed many blockchain-based identity applications,

such as Onename [30], ShoCard [31], and Ana [32]. They used

public blockchains to keep track of users’ identity attestations,

which were claimed to be invulnerable and easy to use.

Moreover, to leverage biometric authentications for

blockchain approaches, research has accentuated mobile

hardware performance, such as energy consumption and

computational delay [33, 34].

Even though blockchain-based identity approaches still rely

on the trust we hold in the identity issuers, which may escalate

into a circular trust problem when some of the issuers are

compromised, we believe decentralization does, to a certain

extent, resolve the centralized ownership of personal identities.

For example, companies and organizations will no longer own

their users’ or customers’ personal information. They only

know if their users satisfy a particular requirement. One can

choose only to reveal enough amount of their identity

attributes for verification. In other words, decentralization can

maximize the need to preserve the users’ or customers’

privacy.

C. RELATED WORK

Quantum decentralization has been discussed for years since

the vision of quantum networks arose. QKD has been

developed using hybrid quantum-classical networks, based on

which decentralized quantum approaches (e.g., quantum

blockchains) have been developed. For example, a data

transmission protocol based on BB84, the first QKD protocol,

and distributed ledgers has been proposed [35] to maximize

the security of key transmission. Quantum computing

naturally avoids some classical attacks without extra effort.

For instance, in [36], a decentralized quantum cash system,

qBitcoin, has been proposed based on quantum teleportation,

which naturally prevents double-spend attacks. In [37], the

authors propose a quantum blockchain scheme with the

concept of a quantum coin based on quantum entanglement,

no-cloning theorem, and a delegated proof of stake consensus

protocol. In [38], a decentralized base-graph routing protocol

has been defined based on quantum repeater networks. It

allows finding the shortest paths in quantum networks using

only the local knowledge of the network nodes. Other methods

of adapting quantum technologies to different blockchain

components and their advantages in a quantum setting have

also been explored [15, 16, 17, 39].

There are various quantum approaches to achieving

genuine authentication, such as quantum fingerprinting [40]

and single-photon authentication [41]. An authenticator can

determine whether a quantum identity matches a real one in

multiple ways. For example, the quantum fingerprint is

analogous to the classical digital fingerprint that associates a

long string (an original string) with a much shorter string (its

fingerprint), such that any two different long strings can be

distinguished by only comparing their fingerprints.

However, there is no existing research on authentication

applications based on quantum blockchain technology. As

quantum computers are threatening the classical approaches,

these applications need a way to adapt to the new challenges

in the quantum era. Access control and authentication issues

should be solved before decentralized quantum applications

can be achieved. This article explores the feasibility of

migrating the classical blockchain-based identity framework

to quantum blockchains and proposes a conceptual design.

III.

PRELIMINARIES

In this section, we introduce and review the preliminaries

about the technologies that QBIF is based on. Table I gives the

common symbols used in this article.

TABLE I

SYMBOLS IN THIS ARTICLE

Symbol

Meaning

We use a Greek letter inside the bra–ket notation to

represent a quantum state. A quantum state could be

multiple qubits or one qubit (e.g., !"

$ !%%

&'(')'*

The Pauli gates (the basis gates commonly used for

quantum operations) and the identity gate

. Quantum

gates can be expressed as complex matrices.

& $

% ,

, %

( $

% ./

/ %

) $

, %

% .,

* $

, %

% ,

-. A symbol in a rectangle represents a gate in a

quantum circuit (See Figure 1 for examples).

A controlled-not gate. It applies

gate to the target

qubit if the control qubit is in state

. In a quantum

circuit, it is represented by a dot connecting an

gate

(see Figure 1). The qubit associated with the dot is the

control qubit. The qubit with the

gate is the target

qubit.

2'3'4'5

Quantum operations, including quantum circuits,

oracles, and measurements (4), are represented as

uppercase italic letters. A measurement of a quantum

state yields a classical result.

⨂#

A quantum circuit used to prepare a quantum state with

100% amplitude on a classical sequence of bits ".

(e.g., 2

!%%

$ 6&7*8!%%

$ !,%

). A quantum

circuit is a sequence of quantum logic gates (e.g., Pauli

gates) to operate on quantum states, analogous to

classical logic gates for classical digital circuits.

An oracle (or a quantum transformation). An oracle is a

function to transform one quantum state into another,

often a “black box” function. The subscript ;

represents a classical function ;

<=% ',>

? =%',>

(e.g., the constant oracle and the balanced oracle in

Deutsch-Jozsa Algorithm [42] where @ $ ,). Note

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VOLUME XX, 2020 5

that in a quantum system, applying a function to a state

is simply the matrix multiplication of the function (a

matrix, e.g.,

) and the state (a vector, e.g.,

), so we

usually just write

instead of

6!:

"'A

A quantum state consisting of the classical output of ;

with the inputs of " and A.

B!%

C!%%

A quantum state part with its amplitude. In general, the

measurements of quantum states are probabilistic. The

square of the coefficient (amplitude) indicates the

probability of the measurement result being the bits

inside that bra–ket (e.g., 0 or 00). Note that these two

symbols are not complete unless B $ , and C $ ,.

For B!%

, the probability of the measurement result

being 0 is B

(

. For C!%%

, the probability of the

measurement result (two qubits) being 00 is C

(

. If all

the possible measurement results are concatenated by

“D” signs (e.g., B

D 0E

D 0C!,%

D 0F!,,

), all

probabilities would be listed in the equation and B

(

D C

(

D F

(

$ ,.

QUANTUM STATES AND THEIR OPERATIONS

A quantum bit (qubit) is the elementary unit of quantum

information analogous to a bit in classical computers. While

a bit has an exact value of either 0 or 1, a qubit could be in a

linear superposition of both values. A qubit is usually

expressed as a linear combination of

(

and

(

with their

corresponding amplitudes/possibilities (or a unit vector in a

complex Hilbert space):

(

+ ,

(

- .&)

(

+ ",/.%

. (1)

where

and

are the amplitudes of

(

and

(

. They

suffice if

&,&

- &.&

+ )

&,&

and

&.&

are the probabilities

that

(

will be measured as

(

, respectively. A

quantum state can be expressed with a single qubit or multiple

qubits.

(

are the basis states in the computational

basis. Each state preserves a probability distribution of all the

measurement outcomes. For example, a 2-qubit state can be

expressed as

(

+ ,

(

- .

(

- 0

(

- 1&))

(

Quantum gates do operations on quantum states. Quantum

gates to quantum states are like Boolean operators (bitwise

operators) to bit strings. Quantum states are mathematically

expressed as complex vectors (e.g.,

(

)

) and quantum

gates are expressed as complex matrices (e.g., the Pauli gates

4/5/6

). It has been proven that any quantum gate can be

expressed as a weighted sum of the Pauli gates (

4/5/6

which is a common form to express gates. Assume every

initial qubit is in the state of

(

. Applying

gate to the

second qubit of a 2-qubit state can be expressed as

(

+ 74

(

+ &')

(

. Operations between quantum

states and gates are matrix multiplication. For example,

applying

gate to

(

can be expressed as the matrix

multiplication of

and state vector

(

4&'

(

' )

) '

)

+ &)

(

. Operations between gates and

gates (or states and states) are tensor products. For example,

(

8&)

(

)

'/)/'/'

+ &')

(

. Note that, for

simplicity, these notations are equivalent:

(

989&:

(

A quantum circuit is a complete operation for a particular

purpose, which usually contains a sequence of quantum gates

and measurement operators. Figure 1 shows an example

quantum circuit that achieves quantum teleportation with

three qubits. Solid lines are quantum wires, and double lines

are classical wires.

;

is a quantum gate called Hadamard

that maps the basis states (i.e.,

(

and

(

considering one

qubit) to uniform superposition. A uniform superposition

describes a state when it has evenly distributed amplitudes

on all its possible terms (e.g., considering one qubit in (1),

, +

and

. +

). A meter in a rectangle (the two

rectangles after

(

in Figure 1 represent a measurement

operation.

and

with classical wires (on the right of

Figure 1 are classically controlled gates that use classical bits

(measurement results of the top and middle qubits) as control

bits to determine whether to apply the

gate to the

bottom qubit.

FIGURE 1.

A quantum teleportation circuit.

QUANTUM TELEPORTATION & NETWORKS

The information encoded in a quantum state can be

transmitted (actually teleported) to a remote party through

entanglement. Entanglement is a quantum effect in which

qubits are intrinsically linked even when long distances

separate them. This kind of information transmission is

called quantum teleportation.

It is called teleportation because photons are not really

transmitted in this process. Still, the information is received.

Unfortunately, the information at the sender’s side is

destroyed after the process. For example, for teleportation

from Alice (the sender) to Bob (the receiver), only the state

amplitudes are shuttled to Bob’s state from Alice’s. Alice’s

state information is destroyed (original amplitudes are lost)

after the teleportation due to a measurement in the process.

The process of quantum teleportation can be simply

described as follow (together with Figure 1):

1) Before the transmission, Alice and Bob create an

entangled qubit pair together, either through a third

party or themselves (i.e., operations before

(

Figure 1 creates an entangled pair for the middle and

bottom states). Alice and Bob each take one qubit

from the pair. Suppose Alice takes the middle qubit

and Bob takes the bottom qubit. The top qubit

represents the state that Alice wants to transmit. Note

that the top qubit can be in any arbitrary unknown

state.

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 6

2) Alice performs the controlled-not gate

and

;

gates to her two qubits, as shown in Figure 1 (between

(

and

(

3) Alice measures her two states (the two meter symbols

after

(

in Figure 1).

4) After measurement, Alice sends her results to Bob

over a classical communication channel (the double

lines in Figure 1).

5) Bob then chooses to perform

gates (or not)

according to Alice’s results to transform his qubit to

the state that the top qubit was in. For example, Bob

should apply

gate to his qubit (the bottom qubit) if

the measurement result of Alice’s middle qubit is one;

otherwise, do nothing. Similarly, he should apply

gate to his qubit if the measurement result of the

Alice’s top qubit is one. After these operations, the

bottom quit will have the same amplitudes that the top

qubit was in.

Current quantum communication and networks are mostly

based on quantum teleportation. Recent studies have shown

teleportation of quantum states with over 90% fidelity [43].

Fidelity describes the quality of teleportation, that is, how

close the teleported qubit is to the original. There are also

other researches enabling quantum state transmission. For

example, Bennett et al. proposed a quantum communication

method called remote state preparation (RSP) [44] based on

quantum teleportation. The communication of RSP encodes

one bit per qubit, by which a transmission of quantum

information (a known state transmission) is realizable.

However, Alice and Bob can also communicate over

classical channels and remake the state at Bob’s side directly

if they want to transmit a known state. Even though robust

quantum teleportation implementations are still under

exploration, they inspire the vision of a quantum network and

the quantum internet. Furthermore, in literature, a network

constituted by QKD is also envisioned as an early stage of a

quantum network.

It is worth noting that a peer-to-peer quantum network is

assumed in almost all quantum blockchain discussions,

including this article. In other words, a private (direct or

indirect) quantum channel is assumed to be established

between all pairs of the network nodes. Such assumptions

have been commonly used as a way of reasoning for quantum

networks and protocols [13, 45].

QUANTUM PKI

A user in a PKI has two types of keys: a public key that can be

shared with anyone and a private key that is only kept by the

user. The public key and private key are always in a pair. A

public key can be used to encrypt a message, and only the

corresponding private key can be used to decrypt it. For

example, when Alice wants to send a secret message to Bob,

Alice can use Bob’s public key to encrypt the message and

send it to him. Then, only Bob, who has the private key, can

decrypt the message and see the plain text. Moreover, a private

key can also be used to sign a message for non-repudiation.

For example, when Alice wants to prove that she is the sender

of a message, she uses her private key to sign the message

before publishing it. Then, anyone with Alice’s public key can

verify the source of the message by matching it.

PKI is widely used to authenticate network activities (e.g.,

SSH, HTTPS, blockchains, digital identities). For identity

management, it is used to generate a unique digital identity for

a user by binding the user information (e.g., username, ID)

with a public key. The binding is usually established by a

certificate authority (CA) through the registration or sign-up

process. Moreover, by signing with the user’s private key, a

user can prove the ownership of a message. By signing with a

CA’s private key, a CA can issue a statement (e.g., an

attestation about an identity).

Technically, PKI is based on one-way functions, typically

trapdoor functions. A trapdoor function, say,

=">%

, is a

function that, when given

=">%

and the secret

, it is easy to

calculate the variable

. Without the secret

, it would be

extremely difficult or impossible to get

. RSA is one well-

known example that is based on trapdoor functions. Since the

classical trapdoor functions are endangered by the

development of quantum computers and algorithms (e.g.,

Shor’s algorithm [5] and Grover’s algorithm [6]), quantum-

enhanced trapdoor functions have been proposed, which led to

the development of quantum PKIs. They use different types of

keys by design (e.g., quantum keys in the form of quantum

states or classical keys that consist of classical sequences of

bits).

Either with quantum keys or classical keys, the encryption

and signature schemes for quantum states enable quantum

PKIs. For example, in [46], quantum keys based on a quantum

one-time pad are used to encrypt quantum states. Moreover, a

symmetric-key encryption scheme (where the keys for

encryption and decryption are the same) for quantum states

(called “private quantum channels”) has been developed by

using a pre-shared single use secret key (also referred to as

one-time pad) [47]. It constructs a private communication of

quantum states on an insecure one-way quantum channel

(using a

-bit classical key to securely transmit

qubits)

[47]. Such private channels enable asymmetric-key encryption

and, thus, quantum PKIs. For instance, in [22], a one-way

quantum identity authentication has been developed to encrypt

quantum states with classical keys. In [48], public-key

encryption and authentication have been developed using

quantum public and classical private keys.

Here, we briefly review the quantum PKI schemes

presented in [48, 49] for quantum-state encryption, signature,

and authentication. The notations introduced here will be re-

used for our conceptual design of QBIF presented in Section

IV. The schemes are based on trapdoor one-way quantum

transformations (OWQT) [48, 49]. Trapdoor OWQT is a

quantum variant of a classical trapdoor function. The

following paragraphs explain how the public and private keys

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 7

are made based on a trapdoor OWQT and how they are used

for quantum encryption, signature, and authentication.

Public-key encryption: The definition of the trapdoor

OWQT

%&'(

[49] can be represented as (see Figure 2)

%&'(

"&B

(

9&'

(

9&'

(

% + &B

(

9&C

*/B

(

9&=

*/B

(

. (2)

where

="*/B%

is a classical trapdoor one-way function with

a random parameter

C"*/B%

is another classical function.

(

is an initial qubit. Particularly,

="*/B%

C"*/B%

, and

constitute a further trapdoor function as a whole, say,

D"*/B%

[49].

D"*/B%

is then used to implement the quantum trapdoor

OWQT

%&'(

D"*/B%

should satisfy:

• easy-to-operate: given a random parameter

as the

trapdoor of

="*/B%

and

C"*/B%

, both

="*/B%

and

C"*/B%

can be computed efficiently;

• hard-to-invert: given the values of

="*/B%

and

C"*/B%

, both

and

cannot be efficiently computed;

• easy-to-invert with the trapdoor: there exists a trapdoor

(secret information)

for the trapdoor function (the

trapdoor OWQT

%&'(

). Given the trapdoor

, the

message

can be efficiently computed from

="*/B%

and

C"*/B%

, and

can be efficiently computed from

="*/B%

and

C"*/B%

In other words, with secret

, it is easy to compute

from

(2) but extremely difficult otherwise (i.e., one-way function).

Suppose we have found such function

D"*/B%

and we now

want to use it to implement the trapdoor OWQT

%&'(

as a

quantum circuit. As shown in Figure 2, we can implement it

by translating

="*/B%

and

C"*/B%

to three oracles

)

and

[49]. By cascading the three oracles, we get the

quantum circuit for the trapdoor OWQT

%&'(

FIGURE 2.

The general quantum circuit for a trapdoor OWQT.

With the trapdoor function OWQT

%&'(

, the functions

and

are public. They can be prepared by the receiver so that

only the receiver has the trapdoor

. Thus, the functions of

and

can be considered as the receiver’s public key (or the

tools to create public keys) and the trapdoor

as the receiver’s

private key. With these key generation processes, encryption

and decryption of a quantum state

(

can be done as follow:

1) Bob finds a trapdoor function

and announces its

components

and

as a public key. He keeps the

trapdoor

to himself.

2) Alice wants to send an encrypted quantum message

(

that only Bob can read. She generates a

%&'(

according to Bob’s public key.

3) Alice adds the parameter

and two initial qubits to

(

and gets

(

4) Alice encrypts

(

by the

%&'(

(2) and

obtains the ciphertext:

(

&C"*/B%

(

9&="*/B%

(

5) Alice sends the ciphertext to Bob.

6) Bob decrypts the ciphertext with

There are two cases of decryption [49]. Here, we directly

show the decryption transformation as

"&?

(

9&C

*/B

(

9&=

*/B

(

+ &?

(

. (3)

Signature: Even though we have the public key and

private key pair, the quantum digital signature is unlike the

classical digital signature. Classically, we can sign a message

and send it out. Anyone with our public key can verify the

message’s source without our intervention. However, the

quantum signature process introduced here is an interactive

digital signature protocol.

Suppose Alice has a trapdoor function

, consisting of

and

(2). Here, we represent the variables as bit strings:

'/)G

+, -

+ F'/)G

, where

F'/)G

+, -

is a bit string of

length

H - I

with

J F'/)G

(

bits) and

J F'/)G

(

bits). Similarly,

F'/)G

consists of

J F'/)G

and

F'/)G

. That is:

+ FB

. (4)

where

FK/LG

denotes the concatenation of two bit-strings,

and

. As discussed,

can be considered a public key. In

this case, Alice has the private key (the trapdoor, say,

The process to sign

(

and verify the signature is as follows:

1) Bob generates

J F'/)G

randomly.

2) Alice generates

J F'/)G

randomly and receives

from Bob. Now Alice has

and

and the trapdoor

MNOPO

can be used to compute the inverse of

+ "B

. Alice then signs the quantum

message

(

with

and function

(i.e., prepared as

) as in (5) and sends it.

(

56+

+ &*

(

9&D"F*/B

(

. (5)

where

Q denotes a state prepared with

- I

number of

(

. For example,

(

is short for

&'''

(

3) Bob notifies Alice of the receipt of the quantum

message.

4) Alice announces

and

5) To verify the signature, Bob computes

D"B

(

public) and checks if the first

bits (of

F'/)G

) are

. If yes, it proves Alice has the trapdoor

. Bob

then performs the transformation as in (6) to obtain the

message (

and

are known to Bob by this step).

(

9&D"*/9B

(

S &*

(

9&'

56+

Q. (6)

Finally, Bob accepts the signature only if the last

- I

qubits are all in state

&'(

(

belongs to Alice). Any signature

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 8

that uses

to generate

9&D"*/B

(

without the interactive

process would be invalid. Note that this signature protocol

does not support multiple verifications. The signed quantum

state

(

9&D"*/B

(

is invalid after the quantum message

(

is extracted. Therefore, this kind of signature can only be

validated once. However, it is possible to obtain a local copy

of the signed quantum state (a known state) [50]. The

verification then only invalidates the local copy.

Usage: It is worth noting that to construct a complete user

account, the quantum PKI is used differently in quantum

blockchains than in classical computing. The access control

in quantum blockchains (i.e., ownership of an on-chain state)

is assured by interactive signatures on the index of an on-

chain state (Section IV). Nonetheless, it is also important for

the processes of identity attestation and authentication of

QBIF (Section IV). There are many more researches on

quantum PKI [46, 47, 48, 49]. For simplicity, Equations (2),

(3), (5), and (6) are used in this article to respectively

represent quantum public-key encryption, decryption,

quantum signature, and signature verification.

A CHAIN OF QUANTUM STATES

A quantum blockchain can be constructed by a chain of non-

tempering and traceable quantum states. Based on quantum

entanglement in time, we briefly introduce the scheme of

quantum blockchains in [13] as an example. Note that this is

a highly simplified version of the classical blockchain. One

quantum state constitutes one block. In other words, this

design assumes one transaction per block.

Before going to the chain of quantum states, we briefly

explain quantum entanglement. The notion of a temper-free

chain is inspired by the non-separability of a quantum system

(entanglement). Quantum entanglement in time can be

viewed as a temporal quantum effect where states are

interdependent across time.

If two qubits are entangled, their measurement outcomes

are correlated. If we measure one of the qubits, the other

qubit instantly collapses into a definite state and would yield

a correlated outcome. For example, the entanglement of the

Bell states

(

and

(

may be such that the measurement

result of

(

is exactly the same as the measurement result of

(

. The measurement outcome of them is random, either

both being 0 (

&''

(

) or both being 1 (

&))

(

). Each outcome has

a 50% chance.

(

+ &>T

(

;<<

>,>;##

. (8)

It is also possible for two Bell states

(

and

(

to be

entangled such that the measurement result has a 50:50

chance of being

&')

(

&)'

(

Multipartite GHZ (Greenberger-Horne-Zeilinger) states

generalize the qubit entanglement to achieve multi-qubit

entanglement, in which all the involved states are entangled

with each other [51, 52].

Going back to the chain of quantum states, multi-qubit

entangled states can be recursively added into a growing

chain in chronological order by entanglements in time [13,

53]. This chain of quantum states can be used to constitute a

primitive quantum blockchain. For simplicity, a 2-bit string

is used here to represent the data in a block (it can be

extended to larger bit strings by multi-qubit entanglement,

but still, it depends on the maximum qubit a quantum

computer can support). Here, we prepare them into a

temporal Bell state:

?#?"

(

>;?

>,>64#7

>;#

>;?

(9)

where

Q is the negation of

. Now we can create the next

temporal Bell state (next block) entangled in time with this

state. These two Bell states do not actually coexist, but the

second Bell state is correlated with the first one (i.e., the

current state is correlated with its previous existing state).

Such states were physically generated in the experiment

introduced in [53]. Adding subsequent states to them forms

a chain of Bell states in chronological order.

Now we add timestamps. A delay line of time

is applied

to each Bell state’s creation. Each state is marked by its

creation time, which becomes the block’s timestamp. Let the

creation time of the first Bell state (genesis block) be

X + '

and the time of the next state (next block) be

X + W

. The

genesis block and the next block can be fused into a four-

photon GHZ state:

?#?"

(

<B(

>;?

>,>64#7

>;#

>;?

. (10)

is the genesis block’s timestamp, and

is the second

block’s timestamp. Recursively, the blocks become a chain

of entangled states (a non-tempering and traceable history of

a state). At

X J F'/W/@W/Y/$WG

, the chain of quantum states

can be represented as

<B(B( B "(B "(B :(DB

E4#

(BE(

)

(

9&*

(

9&*

(

9&*

)

Z9&*

"'*$

E4#

(

9&*

[)

(

)

Z&*

"'*$

E4#

(

. (11)

Each pair of

"+*$

6F4#7(

\ J

@/]/Y/@$

F'/)G

is a block.

"G4#

is the 2-bit data in a block. The

superscripts

represent the block timestamps. For example,

suppose the first two blocks contain bit strings 00 and 10,

and the first and second blocks are

(

<B(

and

(

(B"(

respectively. With two blocks, the chain is

<<#<

(

<B(B( B "(

Adding a third block with value

))

produces

<<#<##

(

<B(B( B "(B "(B :(

It is worth noting that entanglement in time is distinct from

the more commonly used space-based entanglement [54] in

which photons in different locations are entangled. The

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VOLUME XX, 2020 9

entanglement in time can be viewed as a quantum networked

time machine [13].

Besides using GHZ states, quantum blockchains with

other kinds of states have also been experimented with. For

example, Banerjee et al. create a chain of quantum states

using multiparty entanglement of quantum weighted

hypergraph states [55]. Bennet et al. propose a quantum-

enabled blockchain architecture using quantum information

encoded in light (quantum states of light) [56]. Theoretically,

the chain of hypergraph states or quantum states of light can

also be used in place of the chain of GHZ states and become

the data structure of a quantum blockchain using

entanglement in time.

Obviously, currently implementable block size and

potential chain size are not comparable with the classical

blockchains. However, as quantum technologies develop, we

believe quantum blockchains can be extended. More

limitations and challenges of quantum decentralization are

introduced in Section V.

PRIMITIVE CONSENSUS

In a quantum blockchain, each blockchain node hosts a copy

of the chain of quantum states represented in (11). Thus, a

consensus protocol is needed to add new blocks securely. It

should be able to verify the correctness of the newly added

blocks and seek an agreement from all nodes on the validity

and sequence of these new blocks. θ-protocol [45] and

quantum random number generator (QRNG) have been

proposed to solve such problems. QRNG guarantees the true

random selection of a verifier node. True randomness assures

fairness and thus should be agreed upon among nodes. The

selected verifier node is then responsible for performing a

verification test of the new block and adding it to the chain.

θ-protocol is then executed to ‘broadcast’ the new block to

other parties. In other words, nodes in the blockchain agree

on the true randomness instead of solving a cryptographic

puzzle or staking coins (e.g., Proof-of-work, Proof-of-

Stake). This is similar to leader-based consensus protocols

[57]. The fundamental probabilistic property of quantum

mechanics gives QRNG the ability to create true

randomness, which can be clearly modelized and controlled

for perpetual unpredictable randomness, contrary to the

predictable randomness generated by classical deterministic

processes such as pseudo-random number generators

(PRNG).

Note that the QRNG machine today may have statistical

biases due to noisy quantum hardware and is not realistic for

use. We assume such bias can be tackled in the future.

Nonetheless, the instantly produced randomness may not be

able to guarantee simultaneous additions of new blocks. A

complete scheme of consensus mechanisms for quantum

blockchains is still under exploration [23, 45]. After the

verifier (block producer) selection, the verifier node initiates

the verification test (e.g., θ-protocol), which allows each

node in the network to verify if a source is distributing a

correct state, even in the presence of untrusted nodes. The

verifier node finally adds the new block to its local quantum

blockchain copy and broadcasts the addition. There are still

many limitations to the implementation of quantum

broadcasting. More details about broadcasting can be found

in Section V. Based on QRNG and θ-protocol, we achieve a

primitive consensus process for QBIF, which is discussed

next.

IV.

QUANTUM BLOCKCHAIN IDENTITY FRAMEWORK

The vision of QBIF is to achieve secure pseudonymization,

which preserves privacy and prevents forgery. Users control

their own identities and use them without revealing

unnecessary information (self-sovereign identities). At the

same time, identities are secure and genuine under a

decentralized quantum setting. In this section, we introduce

various aspects of the architecture of QBIF: roles, quantum

identity attestations, quantum blockchains, authentication,

and consensus protocols.

ROLES

In this article, ‘identity’ includes the user’s unique id (e.g.,

username, social security number), attributes (pieces of

information about the user’s identity, e.g., name, age,

balance, address), and attestations (proofs of user statements

about attributes, e.g., ‘birthyear == 1999’, ‘income >

50,000’). We also use ‘public credential’ to refer to a user’s

public identity information (unique id and attestations).

Identity attributes are private to users (owners). Attribute-

based identity authentication, which verifies identity

attributes without revealing additional information, is a

prevalent way to authenticate users with anonymity

(pseudonymization) [58, 59].

Users can prove that they satisfy the conditions set by

identity verifiers without revealing their actual identity

information. Identity verifiers authenticate users by verifying

the issuers’ signatures on the attestations. For example, a

bank may loan money only to users whose annual incomes

exceed $50,000. When the bank (verifier) evaluates a user’s

financial information for a loan request, the bank can verify

the user’s annual income by checking the signature on the

user’s attestation without looking at the user’s actual income

number. Keeping attestations on a blockchain ensures their

authenticity. Identity attributes are private to owners.

Decentralized identity removes the concerns of privacy

violation and single-point-of-failure.

As in the classical approach, there are three roles in QBIF:

identity owners, identity issuers, and identity verifiers.

Identity issuers represent trusted parties such as local

governments or big companies. Issuers issue identities such

as personal IDs or user profiles in an application/software.

They also attest (not issue) the validity of identity attributes

and issue attestations. For example, a bank only issues

attestations about users’ financial information. An attestation

process is started on the user’s demand and finished by an

issuer. The reliability of an attestation depends on the

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VOLUME XX, 2020 10

reputation of the issuer. Only attestations are stored on

blockchains. Ownership is marked by double signatures, as

discussed in Subsection E. Users keep their identities at

discretion (preferably privately) and use only the on-chain

attestations to prove statements about their identity attributes

to verifiers. The verifiers provide services according to the

reputation of the issuers who attested the identity statements.

In QBIF, attestations are kept in the form of quantum states

and are chained together by entanglement. These are called

quantum identity attestations (QIAs). Issuers do the generation

of QIA. Verifiers on user’s demand do authentication of QIA.

Identity owners (users) who want authorized actions from

verifiers must go through authentication and attestation

processes if they have not done that with the issuers.

QUANTUM IDENTITY ATTESTATIONS (QIAs)

Attestations are evidence about users’ identity statements.

They could be in any form (e.g., hash values, encrypted

messages, or bit strings). Here, we assume to keep them in

bit strings for simplicity. QIAs in QBIF are quantum states

containing such bit strings, which could be created by

converting them into qubits [60, 61]. Nonetheless, one user

can have multiple QIAs (for different identity attributes). Let

be the bit string of attestation that consists of

bits; then,

a QIA can be represented as

(

(12)

A QIA should be double-signed (by the owner and the

issuer) before use, and a signed QIA can be represented as

(

as indicated in (13). Signatures are interactively done

between an owner and an issuer (signed with private keys

from both parties) as discussed in Section III.C.

(

has

$ -

@"$ - _%

qubits after double-sign, where

is the length of

and

is the output length of

defined in (4).

(

R + &*

(

9&D

*/B

(

9&D

"*/D

*/B

Q. (13)

The superscripts indicate which party (

: user,

: issuer)

belongs to. A QIA is prepared by an issuer per user

request in the attestation process. QIAs are double-signed (as

(

) and are kept in the chain of quantum states. Signing

with the issuer’s private key indicates that the issuer agrees

with the user’s attested statement. Signing with the user’s

private key demonstrates the ownership of the attestation. No

trusted centralized storage is needed.

QIAs ON QUANTUM BLOCKCHAIN

We assume a quantum network and achieve decentralization

over quantum blockchains. QBIF provides distributed

identity management and a primitive consensus protocol for

coordinating network nodes (consisting of users, issuers, and

verifiers). Nodes are interconnected by quantum

communication channels. As shown in Figure 3, each party

keeps a copy of the chain of quantum states that holds the

signed QIAs chronologically. The list of signed QIAs is kept

on the chain in the form shown in (11).

Issuers and verifiers are candidates for block producers

(e.g., miners on proof-of-work blockchains). The owner of a

QIA and the issuer must double-sign the QIA before it goes

into the block pool, i.e., candidate blocks to be attached to

the chain. Block producers add these blocks to the chain after

a consensus process (Section IV.D). The ownership of the

signed QIA is demonstrated by the owner’s signature, and

the validity of the QIA is marked by the issuer’s signature.

As discussed, the signature could only be done by an

interactive signature process. Any QIA signed without the

consent of both parties is invalid and does not pass the

consensus process.

Once a QIA is put on the chain, the owner can initiate an

action with a verifier by sending the location of the signed

QIA on the blockchain. The verifier determines the

authenticity of the QIA by validating the signed QIA with

the user’s and the issuer’s public keys. No additional

knowledge of personal identity is needed during the

authentication.

FIGURE 3.

Roles and interactions on QBIF.

Note that the level of validity for an attestation can be

defined by an issuer so that a user can meet whatever level a

verifier may require. The level of validity can be determined

by way of issuance or attestation, such as verifying in person,

with biometric readers, via password, online, etc. The level

of validity can be integrated into QIAs by adding extra qubits

describing the level.

Since we are dealing with a primitive quantum blockchain

structure, there are no sophisticated event triggers such as

those used in smart contracts in classical blockchain-based

applications. Thus, part of the communication would be off-

chain, such as the online verification mentioned above. A

hybrid network of classical and quantum communications

would be the most plausible transition from classical internet

to quantum internet as quantum technology develops. QKD is

one good example.

In QBIF, quantum PKI and quantum blockchain processes

are executed on quantum communication channels. Other

interactions, such as off-chain attestations and agreements, are

kept on classical channels. As shown in Figure 4, the network

of QBIF is composed of multiple quantum nodes connected

via a quantum network in a peer-to-peer fashion. The classical

channels are neglected in the figure but coexist with the

quantum channels. Each node is a quantum system hosting a

copy of the quantum blockchain, combined with a classical

system dealing with off-chain communications.

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content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

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VOLUME XX, 2020 11

FIGURE 4.

A QBIF network.

CONSENSUS PROTOCOL

As discussed earlier, consensus protocols of a quantum

blockchain are primitive due to the difficulty of implementing

block producers' election (or competition). The most prevalent

consensus protocols for classical blockchains are Proof-of-

work (mining) in Bitcoin or Proof-of-stake (voting) in

Ethereum. Here, we propose to use QRNG and distributed

verification tests (e.g., θ-protocol) to emulate an initial

consensus protocol for quantum blockchains. QRNG

guarantees true randomness in selecting a block producer

(who is also responsible for validating a new block). Here, the

true randomness of QRNG replaces the fair

competition/election provided by Proof-of-work or Proof-of-

stake. The selected block producer then executes a distributed

verification test to validate the newly added GHZ state (the

new block). The distributed verification process keeps the

quantum system validated even with untrusted network nodes

[45]. Once the verification tests are done, the new block is

added to the blockchain. Then, the new chain is broadcasted

to all network nodes. Together with Figure 5, the following

steps describe the consensus process of QBIF:

1) By now, a double-signed QIA (

(

) has been created by

an issuer and a user.

(

is waiting to be added to the

blockchain. The issuer of

(

initiates the consensus

process and activates a QRNG to randomly select a

blockchain producer among the candidates.

2) A candidate is selected by the QRNG. If the candidate

is unavailable, the QRNG is executed again until an

available candidate is selected. We assume the selected

candidate is trustworthy (i.e., candidates are trusted).

Suppose the 3

node in Figure 5 is available and is

selected. It then takes the role of block producer and

initiates the distributed verification. For example, in

[45], a pass condition and a set of random angles

'/c

are defined in advance,

d J F)/@/UU/$G

represents the measurement basis of node j, and the

verification runs until all the network nodes satisfy the

pass condition. For an ideal GHZ state, the verification

will succeed theoretically with 100% probability.

However, this probability is varied according to

entanglement fidelity.

(

is accepted only when the

majority of nodes pass the condition [45].

3) Once we have a valid

(

, the block producer then fuses

(

into a four-photon GHZ state with the latest on-

chain state (11), which adds

(

to its local copy of the

QIA chain.

4) Then, the block producer ‘broadcasts’

(

to all

network nodes. Note that the verification protocol in

[45] involves more than merely implementing

verification tests. It also links the outcome of the

verification tests, the validated state, to the target state.

In other words, the newly added block has also been

copied and distributed to all other network nodes during

the verification tests. This distribution of the new block

remedies the broadcasting limitations of quantum

networks. This is discussed further in Section V.

FIGURE 5.

A consensus process.

ATTESTATION AND AUTHENTICATION

Identity attestation and authentication are two critical

processes of QBIF. The attestation process produces QIAs,

and the authentication process uses QIAs. In Figures 6 and

7, dashed arrow lines refer to classical communication

channels, and solid arrow lines represent quantum channels.

Attestation process: The attestation process is completed

by collaboration between the user and an issuer. This process

creates QIAs and makes interactive signatures. Figure 6 shows

a step-by-step attestation process. Together with Figure 6, the

following steps describe the identity attestation process:

1) A user initiates the process by requesting an identity

attestation. The user defines the statements about the

identity attributes (e.g., income > 50,000). The issuer

validates the user’s identity attributes. This step can be

done over a classical communication channel.

2) The issuer prepares the QIA

(

(12) and sends it to the

user over a quantum communication channel.

3) The user receives

(

and starts the interactive signature

(as discussed in Subsection 3.3) with the issuer.

(

first interactively signed with the user’s private key and

then with the issuer’s private key (13). The interactive

signatures prove the ownership and the validity of the

QIA. After

(

is signed from both sides,

(

is ready.

4) The issuer initiates the consensus process by activating

the QRNG.

5) The selected block producer starts the distributed

verification tests. If the tests are passed,

(

is added to

the QIA chain and is broadcasted to the network.

This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

VOLUME XX, 2020 12

6) The block producer sends the location

(

in the

blockchain to the user using a classical communication

channel. Since there is no available decentralized

identifier (DID) to identify users in QBIF (which is

generally used by blockchain-based identity), the user

keeps the signed QIA's location. It is shown to the

verifier in the authentication process and used to localize

the user’s signed QIA. The user can claim ownership of

this signed QIA by private key.

FIGURE 6.

An attestation process.

Authentication process: The authentication process

happens between a user and a verifier when the user requests

an authorized action. It requires a signed on-chain QIA

corresponding to the action’s requirements. The verifier

extracts the signed QIA and uses it to authenticate the user.

As shown in Figure 7, the following steps describe the

authentication process:

1) A user requests an authorized action provided by a

verifier, which initiates the authentication process. The

verifier verifies whether the user satisfies the

requirement (e.g., if the user’s annual income exceeds

$50,000 when applying for a loan).

2) The user interactively signs the QIA location

(as

&$W

(

9&="$W/B

IK-

Q) with the verifier using the same

private key as the one used for signing the QIA and then

sends it to the verifier. This signature of location

proves the user’s ownership of the private key used to

sign the QIA. As discussed in Subsection III.C, only an

interactive signature process can guarantee a signature's

validity (not someone pretending to own this signature).

Therefore, the user must interactively sign and send the

QIA location to the verifier through a quantum channel.

3) The user announces his/her public key if necessary.

4) The verifier extracts the identity location

according

to (6). By

, the verifier finds and obtains the signed

QIA

(

5) The verifier verifies the signatures of

(

with the

issuer and the user’s public key. If the signature is valid,

the verifier uses

to determine the authentication

result. Based on (6) and (13), the extraction and

verification of

(

is described in Algorithm 1.

6) If the process succeeds, the verifier makes authenticated

communications with the user (Section III.C) and

proceeds with the requested service. (e.g., the verifier

successfully verifies that the user’s income exceeds

$50,000 and proceeds with the subsequent loan

application procedures.)

Algorithm 1. Extract and verify a QIA

Quantum transformation: 9

)*+,-

Input: !"

'!GH

0!;6GH 'A

/_1

8I0'J'A

0'A

(

' A

/_1

'0A

(

/_1

FIGURE 7.

An authentication process.

SYSTEM SECURITY

The security of QBIF is mainly based on the quantum

trapdoor one-way functions (2) and the secure nature of

quantum physics (“unconditional security”). Here, we

discuss the security aspects of QBIF:

Quantum-proof: As discussed, classical blockchains'

security is vulnerable to quantum computing. Quantum

blockchains are immune to any notable quantum and

classical attack.

Data integrity: Classical blockchains use hash functions

to chain blocks (and Merkle trees to organize transactions)

and thus are sensitive to data tampering. If a random on-

chain block is tampered with, all its following blocks become

invalid because each block points to its previous block. The

link of hash values is broken from the tampered block to the

latest block. For quantum blockchains, such sensitivity has

been kept and amplified by entanglement. One change to a

single block could demolish the whole copy of the state chain

[13, 24].

Anti-spoofing: Assume that an attacker wants to perform

a spoofing attack, masquerading as a user to claim the user’s

on-chain attestations. The attacker’s goal is to pass an

authentication process fraudulently. Suppose the attacker has

infiltrated the quantum channel between the user and the

1: #Superscript denotation: (!: user, ": issuer, !#$: QIA location).

3: #Extract %&'( by the issuer’s public key

4: %&'

) %&'*%+

,&-.

/' *%+

,&- +

,&-.

/-.

/0 1 %&'*%+

,&-.

/'*%2'

6: #Extract %&'*%+

,&-.

/'*%2' by the user’s public key

7: ,.

/ ) +,.

8: if .

)) .

*33*4,%&'*%+

,&-.

/'*%2'- "56 78

()&*

/*"9*%2'

9: then

10:

11: #Extract %5:'*%;,5:- .

"_(

/0 by the user’s public key and verify signatures

12: %5:'*%;,5:- .

"_(

/0*1 %5:'*%2'

13: <.

"_(!

= ) +,.

"_(

14: if .

"_(

)) .

"_(!

*33*4,%5:'*%2'-"5678

()&*

/*"9*%2'*33*.

"_(

)) .

15: then

16:

17: %&'*%+

,&-.

/'*%2' 1 %&'*%+

,&-.

/' 1 %&'*%2' 1 %&'

18: return %&' #Succeed

19:

20: end if

21:

22: end if

This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

VOLUME XX, 2020 13

verifier (Steps 2 and 3 in Figure 7). The attacker can now

intercept the communication of the QIA location. However,

the attacker still needs to interactively sign it with the

verifier. If the attacker uses his/her own private key and

sends his/her public key, the verifier is not able to extract the

signed QIA by this public key and

(5) (6).

LMMLN+O1

of the

signed QIA location is not the same as

I2O1

of the signed

QIA.

Privacy: On-chain attestations are proofs of statements

about users’ identity attributes without actual identity

information (pseudonymization). Such granular statements

would not reveal much information, even if leaked.

Pseudonymization protects privacy through the non-

correlation principles [58].

CHALLENGES AND LIMITATIONS

Quantum blockchains are naturally immune to quantum

attacks on classical algorithms. It is exciting to see the

possibility of layering blockchains on a quantum system,

even though it is not pure quantum (but a hybrid with

classical systems). In the QBIF conceptual design, every

preliminary technology has been explicitly shown to be

experimentally realizable, even though some are only in their

simplest form. The proposed conceptual design does not yet

meet immediate deployment requirements, but it shows a

visible path toward realizing a decentralized quantum

application. Nonetheless, many challenges and limitations of

quantum approaches are inevitable at this stage. We discuss

the main challenges and limitations of QBIF next.

A. LACK OF IMPLEMENTATION

QBIF and most quantum blockchains lack low-level

specifics, which would contribute to the detailed

implementation of their essential components.

Implementations of many quantum technologies are still

varying and require much further experimentation. Quantum

blockchains are still in their very early phase. Quantum

systems are mostly implemented in simulators or quantum

computers with limited resources. It would not add much

value to the work at this stage by introducing implementation

details.

B. LIMITED QUANTUM HARDWARE

The development of quantum computers has been rapid in

recent years. However, it still needs a significant time before

it can support large or medium-scale computation (and

connection). Current quantum computers are extremely

sensitive to interactions; thus, their computation results

usually have much noise. Besides, quantum states tend to

gradually disintegrate due to quantum decoherence, which

demands quantum error-correction [62]. State discrimination

strategies must be applied to fine-tune the trade-offs between

error rate and information gain [63]. In terms of

authentication, the validation of a whole process would be

determined or significantly influenced by the quantum bit

error rate [22, 41].

C. BROADCAST LIMITATIONS

The ability to distribute entangled states to network nodes is

significant for a decentralized quantum network. Theoretical

analyses on point-to-point quantum communication have

constantly been progressing. Quantum repeaters make

possible long-distance quantum communications over

bipartite quantum channels. However, point-to-point

communication is not enough for a sophisticated network. A

quantum broadcast network would be able to distribute

entangled qubits efficiently. Current quantum broadcast

networks are usually accomplished with the assistance of

classical communications [64]. The upper and lower bounds

of quantum broadcast networks are still limited [65], and a

complex network typically introduces more noise and losses.

D. TEMPORAL ENTANGLEMENT

There are still many open problems with quantum

entanglement in time [13, 66, 67]. Entanglement in time is

based on entangled history theory, which is a substantial

modification of the decoherent history theory (or consistent

history theory). Entanglement in time shares similar

properties with the general entanglement in space [54], but

temporal quantum effects might be highly unstable as time

passes.

E. DIFFICULTY IN ACCESSING STATES

Previous blocks on quantum blockchains based on

entanglement in time are physically no longer existent.

Blocks do not simultaneously coexist. It is only natural to

retrieve the latest block. Previous on-chain states are hard to

access. However, it is possible to transfer the past quantum

correlation between quantum states so that past states can be

obtained, even if they do not coexist simultaneously [50].

Moreover, quantum logic is inherently reversible; thus,

propagating back in time to a previous block will unentangle

qubits and potentially destroy the chain. Fortunately, through

the consensus process, we have many copies of the chain on

the blockchain nodes. Hence, the system is feasible as long

as the majority of the blockchain nodes still keep the copies.

How to make the system more sustainable than this remains

future work.

F. OVERHEAD

Network overhead is significantly increased since signatures

are done interactively between two parties. Signature

processes are common in blockchains. Moreover, many

quantum signatures can only be validated once. This would

significantly increase the number of signature processes and

potentially overload the network nodes. Quantum

fingerprints could replace such interactive signatures to void

this issue.

This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

VOLUME XX, 2020 14

G. SCALABILITY

Scalability is always an issue in quantum applications due to

the current scale of quantum computers and networks. In

terms of quantum blockchains, one transaction per block is

clearly deficient. A complex quantum data structure must be

developed before a quantum blockchain can become

comparable to its classical counterpart.

H. PRIMITIVE CONSENSUS

The current consensus protocol is still primitive, lacking

perfect competition/election rules to create blocks. QRNG is

temporarily used as a basic consensus protocol. However,

QRNG cannot guarantee the normal operation of

simultaneous communications in a decentralized network.

I. LOW EFFICIENCY

Performance issues of quantum blockchains exist in the

information preparation [61, 68], block size [13], and cost-

effectiveness strategies between the used qubit and the

created block [55]. Blockchain size is a challenge for

classical blockchains also due to data explosion.

J. SEMI-DECENTRALIZATION

The classical identity management and this approach require

third-party authorities to verify user attestations and thus are

not actual decentralization but semi-decentralization. The

idea is similar to what a consortium blockchain provides, in

which each member is a group of nodes who believe in the

same authorities [69]. A semi-decentralization could lead to

the dictatorship of resources by a small group of powerful

entities. However, we believe a proper combination of

decentralization and centralization is beneficial since there

are always harmful contents that could inundate the network

without censorship. How an ultimate decentralization can be

achieved in the quantum domain (or in any future form of the

internet) remains future work.

VI.

CONCLUSION

Quantum computers threaten classical blockchains’ security,

and thus quantum blockchains are needed. This article

theoretically analyzes the quantum blockchain technologies

that could be used for a decentralized purpose. We review the

technical evidence and put together a conceptual design for

decentralized quantum identity, which is named QBIF. We

investigate the essential components and the feasibility,

effectiveness, and limitations of QBIF. We complete the

design of QBIF by integrating existing quantum approaches,

such as quantum PKIs and quantum blockchains. Nonetheless,

the conceptual design still has technical gaps in detailed low-

level specifics. Despite the limitations and challenges, we

believe a decentralized perspective of quantum applications is

noteworthy and likely.

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This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/

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Zebo Yang received a B.S. degree in computer

engineering from Guangdong University of

Foreign Studies, Guangzhou, China, in 2012 and

an M.S. degree in computer engineering from

Waseda University, Tokyo, Japan, in 2019. He is

pursuing a Ph.D. in computer engineering at

Washington University in St. Louis, MO, USA.

From 2011 to 2017, he worked as a Software

Engineer at Tencent, Inc., Baidu, Inc., and DJI,

Inc. Since 2019, he has been working as a

Graduate Research Assistant at Washington University in St. Louis. His

research interests include blockchains, quantum computing, network, and

system security, machine learning, the Internet of Things, and wireless

communications.

Tara Salman is an assistant professor of

computer science at Texas Tech University,

Lubbock, Texas, USA. Previously she was a

Graduate Research Assistant at Washington

University in St. Louis (2015-2021) and a

Research Assistant at Qatar University (2012-

2015). She received her Ph.D. from Washington

University in St. Louis in May 2021 and her B.S.

in computer engineering and M.S. degrees in

computer networking from Qatar University

Doha, Qatar, in 2012 and 2015, respectively. Her research interests span

Blockchains, network security, distributed systems, the Internet of things,

and financial technology. She is an author of 1 book chapter, a patent, and

more than twenty internationally recognized conferences and journals.

Raj Jain (Life Fellow, IEEE) received a B.E. degree in electrical

engineering from APS University, Rewa, India, an M.E. degree in

Automation from Indian Institute of Science, Bangalore, India, and a Ph. D.

degree in Applied Maths (computer science) from Harvard University,

Cambridge Massachusetts, USA, in 1972, 1974 and 1978 respectively. He

is the Barbara J. and Jerome R. Cox, Jr., Professor with the Department of

Computer Science and Engineering, Washington

University in St Louis, St Louis, MO, USA. He

was one of the co-founders of Nayna Networks,

Inc., San Jose, CA, USA, a next-generation

telecommunications systems company in San

Jose. He was a Senior Consulting Engineer with

Digital Equipment Corporation, Littleton, MA,

USA, and then a Computer and Information

Sciences Professor at Ohio State University,

Columbus, OH, USA.

Prof. Jain is a recipient of the 2018 James B.

Eads Award from the St. Louis Academy of

Science, the 2017 ACM SIGCOMM Life-Time Achievement Award, and

the 2015 A. A. Michelson Award from the Computer Measurement Group.

He ranks among the Most Cited Authors in Computer Science. He has

authored the Art of Computer Systems Performance Analysis, which won

the 1991 “Best-Advanced How-to Book, Systems” award from the

Computer Press Association. He is a Fellow of the IEEE, ACM and AAAS.

Roberto Di Pietro (ACM Distinguished

Scientist and IEEE Senior Member) is a Full

Professor in Cybersecurity at HBKU-CSE.

Previously, he was in the capacity of Global

Head Security Research at Nokia Bell Labs and

Associate Professor (with tenure) of Computer

Science at the University of Padova, Italy. He

also served 10+ years as a senior military

technical officer. Overall, he has worked in the

cybersecurity field for 23+ years, leading

technology-oriented and research-focused teams

in the private sector, government, and academia (MoD, United Nations HQ,

EUROJUST, IAEA, WIPO).

His main research interests include security and privacy for wired and

wireless distributed systems (e.g., Blockchain technology, Cloud, IoT,

Online Social Networks), virtualization security, applied cryptography,

computer forensics, and data science. Besides being involved in M&A of

start-ups—and having founded one (exited)—he has produced 230+

scientific papers and patents over the cited topics, has co-authored three

books, edited one, and contributed to a few others. He is an AE for

ComCom, ComNet, PerCom, Journal of Computer Security, and other Intl.

journals. In 2011-2012 he was awarded a Chair of Excellence from

University Carlos III, Madrid. In 2020 he received the Jean-Claude Laprie

Award for significantly influencing the theory and practice of Dependable

Computing.

This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and

content may change prior to final publication. Citation information: DOI 10.1109/TQE.2022.3207111

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/