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Journal of Chinese Computer Systems

Research on Parallel Quantum Key Search of Block Cipher

Ye Feng

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

Block cipher has some advantages such as fast,easy to achieve standardization and ease of hardware and software.It has the most extensive application in the computer communication and information system security.This article presents a parallel quantum key search model of block cipher,based on the combination of Grover search algorithm and classical parallel search ideas.Then we put forward the circuit design of corresponding quantum black-box of the typical block cipher.Finally we give a brief performance analysis.

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Block cipher has some advantages such as fast,easy to achieve standardization and ease of hardware and software.It has the most extensive application in the computer communication and information system security.This article presents a parallel quantum key search model of block cipher,based on the combination of Grover search algorithm and classical parallel search ideas.Then we put forward the circuit design of corresponding quantum black-box of the typical block cipher.Finally we give a brief performance analysis.
Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.
To evaluate the security of a symmetric cryptosystem against any quantum attack, the symmetric algorithm must be first implemented on a quantum platform. In this study, a quantum implementation of a classical block cipher is presented. A quantum circuit for a classical block cipher of a polynomial size of quantum gates is proposed. The entire work has been tested on a quantum mechanics simulator called libquantum. First, the functionality of the proposed quantum cipher is verified and the experimental results are compared with those of the original classical version. Then, quantum attacks are conducted by using Grover's algorithm to recover the secret key. The proposed quantum cipher is used as a black box for the quantum search. The quantum oracle is then queried over the produced ciphertext to mark the quantum state, which consists of plaintext and key qubits. The experimental results show that for a key of n-bit size and key space of N such that [Formula: see text], the key can be recovered in [Formula: see text] computational steps.
Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To conduct Grover’s search algorithm, the target cipher algorithm should be efficiently implemented in a quantum circuit. Currently, small quantum computers are difficult to operate with large quantum circuits due to limited performance. Therefore, if a large quantum computer that can operate Grover’s algorithm appears, it is expected that a cipher attack will be possible. In this paper, we propose a parallel structure quantum circuit for the Korean hash function standard (i.e., LSH). The proposed quantum circuit designed a parallel operation structure for the message expansion (i.e., MsgExp) function and the mix function, which are the internal structures of the LSH hash function. This approach shows an efficient result for quantum circuit implementation in terms of quantum resources by reducing the depth of the quantum circuit by about 96% through the trade-off of appropriate quantum resources compared to previous work. This result can be a reference for the implementation of a parallel quantum circuit in the future and is expected to advance the attack timing of the search algorithm for Grover’s LSH hash function.
In order to verify the feasibility of applying the quantum search to the key search of block ciphers,a key search quantum circuit of AES(advanced encryption standard) cipher was designed,including KeyExpansion module,encryption module and comparison module,based on the analyses of its computation processes and computation modules needed to be achieved.The encryption module includes four sub-modules,i.e.,quantum AddRoundKey,SubBytes,ShiftRows and MixColumns.In order to reuse the working quantum bits,the reversible computation is used to eliminate the quantum entanglement effect,and different methods of the reversible computation are adopted to different tasks of the 4 sub-modules in the realization of the quantum encryption module so as to save computation time and quantum memory.The research shows that applying the quantum search scheme to the key search of block ciphers to save square root time is feasible.
In this work, a quantum design for the Simplified-Advanced Encryption Standard (S-AES) algorithm is presented. Also, a quantum Grover attack is modeled on the proposed quantum S-AES. First, quantum circuits for the main components of S-AES in the finite field F2[x]/(x4 + x + 1), are constructed. Then, the constructed circuits are put together to form a quantum version of S-AES. A C-NOT synthesis is used to decompose some of the functions to reduce the number of the needed qubits. The quantum S-AES is integrated into a black-box queried by Grover's algorithm. A new approach is proposed to uniquely recover the secret key when Grover attack is applied. The entire work is simulated and tested on a quantum mechanics simulator. The complexity analysis shows that a block cipher can be designed as a quantum circuit with a polynomial cost. In addition, the secret key is recovered in quadratic speedup as promised by Grover's algorithm.