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Semi-quantum communication: Protocols for key agreement, controlled secure direct communication and dialogue

Chitra Shukla, Kishore Thapliyal, Anirban Pathak

arXiv:1702.07861v1quant-ph

TL;DR

The paper addresses the absence of semi-quantum protocols for key agreement, controlled deterministic secure communication, and dialogue, alongside the question of how much quantum capability these tasks require. It proposes protocols for these tasks and discusses their security and efficiency. The authors conclude that nearly all secure communication tasks achievable with fully quantum protocols can also be performed semi-quantum, at the cost of greater quantum-resource requirements for quantum users.

  • Problem

    The introduction identifies missing semi-quantum protocols for key agreement, controlled deterministic secure communication, and dialogue, and asks how many users need quantum capabilities for secure communication tasks.

    Source: §1 · p. 2

  • Method

    The paper proposes semi-quantum protocols for key agreement, controlled secure communication, and dialogue, and discusses security, efficiency, and reductions to related tasks.

    Source: §1 · p. 2, §3 · p. 8, §6 · p. 14

  • Results

    The authors conclude that almost all secure communication tasks achievable with fully quantum protocols can also be performed semi-quantum, although the proposed schemes have lower qubit efficiencies than similar fully quantum schemes.

    Source: §5 · p. 13, §6 · p. 14

  • Takeaways & Limitations

    The proposals extend semi-quantum communication beyond key distribution and direct communication, with increased quantum-resource requirements for the quantum party.

    Source: §6 · p. 14

    During eavesdropping checking, Alice can learn Bob’s encoding before announcing her own raw key and thereby control the final key completely.

    Source: §2.1 · p. 7

Abstract

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Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first time semi-quantum protocols are proposed for key agreement, controlled deterministic secure communication and dialogue, and it is shown that the semi-quantum protocols for controlled deterministic secure communication and dialogue can be reduced to semi-quantum protocols for e-commerce and private comparison (socialist millionaire problem), respectively. Complementing with the earlier proposed semi-quantum schemes for key distribution, secret sharing and deterministic secure communication, set of schemes proposed here and subsequent discussions have established that almost every secure communication and computation tasks that can be performed using fully quantum protocols can also be performed in semi-quantum manner. Further, it addresses a fundamental question in context of a large number problems- how much quantumness is (how many quantum parties are) required to perform a specific secure communication task? Some of the proposed schemes are completely orthogonal-state-based, and thus, fundamentally different from the existing semi-quantum schemes that are conjugate-coding-based. Security, efficiency and applicability of the proposed schemes have been discussed with appropriate importance.

1 Introduction

The introduction identifies semi-quantum protocols for key agreement, controlled deterministic secure communication, and dialogue as gaps in the existing literature. It frames these proposals against two questions: whether secure quantum communication requires conjugate coding, and how much quantum capability its users need.

1 Introduction

  • Before this work, no semi-quantum protocols had been proposed for key agreement, controlled deterministic secure communication, or dialogue.The introduction also links controlled communication and dialogue to e-commerce, private comparison, and other cryptographic tasks.Source: §1 · p. 2
  • Semi-quantum schemes use fewer quantum resources than fully quantum counterparts, prompting the question of how many users need quantum capabilities for a given task.The introduction asks whether users need abilities such as quantum measurement, preparing states in multiple mutually unbiased bases, or storing quantum information.Source: §1 · p. 2
  • The introduction contrasts orthogonal-state-based schemes with conjugate-coding-based schemes and says the former can perform cryptographic tasks supported by the latter.It also surveys existing semi-quantum work on key distribution, information splitting, secret sharing, direct communication, and private comparison.Source: §1 · p. 2
  • In the conventional semi-quantum model described here, Bob can measure or prepare computational-basis qubits, reflect received qubits, and reorder them using delay lines.The paper adopts this restricted-user model for its proposed schemes.Source: §1 · p. 3
  • The paper organizes its proposals around key agreement, controlled direct communication, dialogue, security analysis, and qubit efficiency.The introduction places these protocols in Sections 2–5, followed by a conclusion in Section 6.Source: §1 · p. 3

2 Protocol for semi-quantum key agreement

The proposed semi-quantum key agreement protocol pairs a quantum Alice with a classical Bob. It targets the stronger form of key agreement, in which both parties contribute equally and neither can manipulate or know the final key before the other parties.

Protocol 1

  • The paper uses the stronger notion of key agreement: each party contributes equally, and no party can manipulate or know the final key before the others.The authors distinguish this from the weaker notion in which both parties merely participate in preparing the shared key.Source: §2 · pp. 3–4
  • The proposed SQKA scheme can be reduced to a semi-quantum key-distribution scheme in which a sender transmits a quantum key deterministically and unconditionally securely.The paper describes this as the first such SQKD scheme.Source: §2 · p. 4
  • The proposed SQKA protocol involves quantum Alice and classical Bob, who may measure or prepare computational-basis qubits or reflect them without disturbance.The protocol is illustrated through three steps, with its working explained through Step1.1–Step1.5.Source: §2 · p. 4, Figure 1 · p. 4

Protocol 1

Protocol 1 uses Bell pairs for semi-quantum key agreement between a quantum Alice and classical Bob, whose operations are restricted to computational-basis measurement/preparation or reflection. Its security discussion describes permutation and verification safeguards, and the protocol can reduce to deterministic semi-quantum key distribution when Alice does not announce her raw key.

Protocol 1

  • Bob measures some travel qubits in the computational basis, encodes his raw key by XORing it with his outcomes, and permutes the encoded and reflected qubits before returning them.Alice prepares n + m Bell states; n are used for key generation and m as eavesdropping decoys. Bob reflects the remaining qubits and measures the others.Source: Protocol 1 · pp. 4–5
  • After the reflected-pair check, Alice announces her raw key and Bob computes Kf = KA ⊕ KB; Eve still lacks Bob’s secret key KB.For the initial |ψ+⟩ state, rA = rB, and Alice can recover Bob’s encoding from the travel-qubit outcomes.Source: Protocol 1 · pp. 5–6
  • If Alice does not announce her raw key, the key-agreement protocol reduces to deterministic semi-quantum key distribution.The authors describe this as a deterministic way for a sender to send a quantum key to a receiver.Source: Protocol 1 · p. 6

2.1 Possible attack strategies and security

  • Bob’s permutation foils the described CNOT attack, which would otherwise let Eve obtain his secret key from the returned encoded qubits.The authors also state that permuting the string can circumvent most attacks they discuss.Source: §2.1 · p. 7
  • Eve’s intercept-and-resend attack identifies which qubits Bob measured 75% of the time and may expose at least 75% of the shared key, while leaving 25% of the key unmatched.Alice and Bob may verify a small part of their shared key to check for this attack; Bob also delays announcing the correct particle order until errors are below a threshold.Source: §2.1 · p. 7
  • The authors state that disturbance, denial-of-service, and impersonation attacks do not affect protocol security, with authentication making impersonation void.Source: §2.1 · p. 7
  • Alice could control the final key if she learns Bob’s encoding before announcing her raw key; delayed permutation disclosure prevents her from identifying the relevant Bell-pair partners.Sharing hashes of their raw keys can also cause the protocol to abort if Alice later changes her key.Source: §2.1 · pp. 7–8
  • Bob could steer the final key by announcing a new permutation after learning Alice’s key, so the authors say to incorporate a hash function.A previously shared hash of Bob’s key prevents him from changing his raw key during permutation announcement.Source: §2.1 · p. 8

3 Controlled direct secure semi-quantum communication

The section proposes controlled direct secure semi-quantum communication with a classical sender and quantum receiver and controller, then describes two protocol variants and their security checks. It also connects the schemes to e-commerce and discusses attacks that Alice’s permutation can thwart.

3.1 Protocol 2: Controlled direct secure semi-quantum communication

  • Protocol 2 uses a tripartite entangled channel: classical Alice encodes her message, while Charlie’s measurement outcome controls when Bob can decode it.Alice and Bob check decoy pairs using Bell-basis measurements and Charlie’s outcome; Bob cannot decode until Charlie announces his measurement result.Source: §3.1 · pp. 8–9

3.2 Protocol 3: Controlled direct secure semi-quantum communication based on cryptographic switch

  • Protocol 3 uses a cryptographic-switch scheme in which Charlie prepares Bell pairs and permutes Bob’s sequence, withholding the information Bob needs to decode.After decoy checking, Bob still cannot decode Alice’s message until Charlie announces the permutation information.Source: §3.2 · pp. 9–10
  • In both controlled direct communication protocols, two of the three parties have quantum resources; reducing that number is left for future work.Alice is the classical party in the proposed schemes.Source: §3 · p. 8, §3.2 · p. 10

3 Controlled direct secure semi-quantum communication

  • A semi-quantum e-commerce scheme lets a classical buyer send an order that the merchant decodes, while the quantum store delivers only after its acknowledgment.The buyer’s permutation, disclosed only after successful transmission, prevents the store from learning or changing the order in the described attack scenario.Source: §3.2 · p. 10

3.3 Possible attack strategies and security

  • Alice’s permutation thwarts the described CNOT attack and prevents an intercept-and-resend attacker from decoding her message, even if initial correlation checks are passed.In the computational-basis resend case, the attacker evades correlation checking but fails at Bob’s eavesdropping check.Source: §3.3 · p. 11

4 Semi-quantum dialogue

The section proposes a dialogue protocol between a quantum Alice and classical Bob, using encoding and measurements that let both recover the other’s message. It also describes a modification for semi-quantum private comparison and discusses security strategies.

4 Semi-quantum dialogue

  • The proposed semi-quantum dialogue protocol has a quantum Alice and a classical Bob, who encodes using computational-basis operations.Bob measures qubits, prepares fresh qubits for his encoded bits, and permutes the sequence; Alice encodes with Pauli operations, and both extract the other’s message from Bell-basis outcomes.Source: §4 · pp. 11–12
  • A slight modification of the dialogue protocol may yield semi-quantum private comparison, where two classical users compare their secrets with help from an untrusted quantum third party.The described task compares whether the users have the same amount of assets.Source: §4 · p. 12

4.1 Possible attack strategies and security

  • The dialogue protocol’s security discussion notes that a prior shared key can also circumvent attacks, but using a key is outside direct communication, motivating particle permutation instead.The paper also notes that hiding initial-state information and sending it through QSDC/DSQC can circumvent information leakage attacks in quantum dialogue schemes.Source: §4.1 · p. 12

5 Efficiency analysis

The efficiency analysis compares the resource costs of the four proposed protocols, finding lower qubit efficiency for controlled three-party schemes than two-party schemes. It also compares semi-quantum efficiency with fully quantum protocols and describes the qubit and decoy requirements.

5 Efficiency analysis

  • Qubit efficiency is the ratio of transmitted c-bits to qubit and classical-communication resources, with decoy qubits counted but associated classical communication excluded.Source: §5 · p. 13
  • For n classical bits sent to a classical user, the quantum user prepares and sends 4n qubits, including 2n decoys for that transmission.The classical sender cannot produce decoys; the remaining qubits support encoding and secure transmission.Source: §5 · p. 13
  • Three-party Protocols 2 and 3 are less qubit-efficient than two-party Protocols 1 and 4; Table 3 reports the proposed protocols’ efficiencies.Source: Table 3 · p. 13, §5 · p. 13
  • Protocol 3 has higher qubit efficiency than Protocol 2, which uses a tripartite rather than bipartite entangled state.Source: §5 · p. 13
  • Protocol 4 has higher qubit efficiency than Protocol 1, with the difference attributed to two-way quantum communication.Source: §5 · p. 13
  • 10% qubit efficiency for SQKA versus 14.29% for QKA; the authors attribute lower efficiency with classical users to unconditional-security requirements.Source: §5 · pp. 13–14

6 Conclusion

The paper proposes semi-quantum protocols for key agreement, controlled communication, and dialogue, then derives e-commerce and private-comparison variants. It concludes that almost all secure communication tasks achievable with two quantum parties can also be performed semi-quantum, at increased quantum-resource cost.

6 Conclusion

  • The proposed semi-quantum schemes cover key agreement, controlled communication, and dialogue; the latter two can be adapted to e-commerce and private comparison, respectively.The authors describe these as first schemes of their kind and state that their security against various attacks is established.Source: §6 · p. 14
  • Almost all secure communication tasks achievable with two quantum parties can also be performed semi-quantum, but with increased quantum-resource requirements and lower qubit efficiency.Source: §6 · p. 14
  • The authors hope the proposed schemes or variants will be experimentally realized and used in devices for daily-life applications.Source: §6 · p. 14
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