[Paper Review] Quantum Public-Key Encryption with Information Theoretic Security

Jiangyou Pan, Li Yang|arXiv (Cornell University)|Jun 2, 2010

Cryptography and Data Security8 references18 citations

TL;DR

This paper proposes a novel quantum public-key encryption scheme with information-theoretic security based on quantum state indistinguishability under chosen-plaintext attack (CPA). It introduces a new public-key structure using GHZ-like entangled states derived from classical functions, achieving security independent of computational assumptions by ensuring any distinguisher's advantage is bounded by inverse polynomial, even against unbounded quantum adversaries.

ABSTRACT

We propose a definition for the information theoretic security of a quantum public-key encryption scheme, and present bit-oriented and two-bit-oriented encryption schemes satisfying our security definition via the introduction of a new public-key algorithm structure. We extend the scheme to a multi-bitoriented one, and conjecture that it is also information theoretically secure, depending directly on the structure of our new algorithm.

Motivation & Objective

• To define information-theoretic security for quantum public-key encryption beyond computational assumptions.
• To address the vulnerability of classical public-key schemes in the post-quantum era.
• To design a quantum public-key encryption scheme that remains secure even against adversaries with unbounded quantum computational power.
• To extend existing quantum encryption schemes with stronger security guarantees based on quantum state indistinguishability.
• To provide a foundation for practical, information-theoretically secure quantum key exchange protocols.

Proposed method

• Introduces a new public-key structure using a classical function F: Ωₙ → Ωₙ as private key and a quantum state ρₖ,ᵢ⁰ as public key.
• Constructs two n-qubit quantum states ρₖ,ᵢ⁰ and ρₖ,ᵢ¹ using Hamming-weight-dependent superpositions and controlled phase flips.
• Employs permutation operators Pₖ to transform states into GHZ-like entangled states, enabling efficient state preparation.
• Uses Z-gate application on qubits to generate the complementary state ρₖ,ᵢ¹ from ρₖ,ᵢ⁰ when Wₕ(k) is odd.
• Defines ciphertext indistinguishability via a quantum circuit family {Cₙ}, requiring that no distinguisher can tell apart E(x) and E(y) with advantage better than 1/p(n).
• Designs a bit-oriented encryption scheme where the plaintext bit b determines whether ρₖ,ᵢ⁰ or ρₖ,ᵢ¹ is transmitted, with security based on the indistinguishability of these states.

Experimental results

Research questions

• RQ1 Can a quantum public-key encryption scheme achieve information-theoretic security under CPA without relying on computational hardness assumptions?
• RQ2 How can quantum state indistinguishability be formalized in the context of public-key encryption to ensure security against unbounded quantum adversaries?
• RQ3 What structural properties of quantum states and classical functions enable information-theoretic security in quantum public-key systems?
• RQ4 Can the proposed scheme be extended to multi-bit encryption while preserving information-theoretic security?
• RQ5 What is the relationship between the Hamming weight of the key and the security of the resulting quantum states?

Key findings

• The proposed quantum public-key encryption scheme satisfies the definition of information-theoretic security under CPA, as any quantum distinguisher's advantage is bounded by 1/p(n) for any positive polynomial p(n).
• The scheme uses a novel public-key structure based on a classical function F and a quantum state ρₖ,ᵢ⁰, where k = F(s), ensuring that the public key reveals no information about the private key s.
• The encryption process leverages GHZ-like entangled states generated via permutation and phase operations, enabling efficient state preparation and transformation.
• The scheme achieves indistinguishability of ciphertexts for different plaintext bits by encoding them into orthogonal superpositions ρₖ,ᵢ⁰ and ρₖ,ᵢ¹, which are operationally indistinguishable without knowledge of k and i.
• The authors conjecture that the multi-bit extension of the scheme is also information-theoretically secure, based on the structural properties of the underlying algorithm.
• The security definition is stronger than prior work, as it removes the restriction to polynomial-size quantum circuits, making it applicable to unbounded quantum adversaries.