Quantum Attacks on 1K-AES and PRINCE

Abstract

By introducing the BHT algorithm into the slide attack on 1K-AES and the related-key attack on PRINCE, we present the corresponding quantum attacks in this paper. In the proposed quantum attacks, we generalize the BHT algorithm to the situation where the number of marked items is unknown ahead of time. Moreover, we give an implementation scheme of classifier oracle based on Quantum Phase Estimation algorithm in presented quantum attacks. The complexity analysis shows that the query complexity, time complexity and memory complexity of the presented quantum attacks are all $\mathcal{O}(2^{n/3})$ when the success probability is about $63\%$, where $n$ is the block size. Compared with the corresponding classical attacks, the proposed quantum attacks can achieve subquadratic speed-up under the same success probability no matter on query complexity, time complexity or memory complexity. Furthermore, the query complexity of the proposed quantum slide attack on 1K-AES is less than Grover search on 1K-AES by a factor of $2^{n/6}.$ When compared with the Grover search on PRINCE, the query complexity of the presented quantum attack on PRINCE is reduced from $\mathcal{O}(2^{n})$ to $\mathcal{O}(2^{n/2}).$ When compared with the combination of Grover and Simon’s algorithms on PRINCE, the query complexity of our quantum attack on PRINCE is reduced from $\mathcal{O}(n\cdot 2^{n/2})$ to $\mathcal{O}(2^{n/2}).$ Besides, the proposed quantum slide attack on 1K-AES indicates that the quantum slide attack could also be applied on Substitution-Permutation Network construction, apart from the iterated Even-Mansour cipher and Feistel constructions.

Quantum Attacks on Type‐1 Generalized Feistel Schemes

“…x 25 2 = x ⊕ R 24 (x 22 2 ⊕ R 23 (x 22 1 )) ⊕ R 25 (x 22 2 ⊕ R 23 (x 22 1 )) (29) From Figure 5 (red line), the function can be described as…”

“…x 25 2 = x ⊕ C 1 (30) where C 1 = R 24 (x 22 2 ⊕ R 23 (x 22 1 )) ⊕ R 25 (x 22 2 ⊕ R 23 (x 22 1 )) is a constant. After an additional 1 round, the value x 22 1 is used as the input of R 26 and the output of R 26 is xored into x 22 2 ⊕ R 23 (x 22 1 ).…”

“…This started with the 3-round Feistel distinguisher proposed by Kuwakado and Morii. [16] After that, more generic constructions, such as Even-Mansour cipher, [17,18] FX construction, [19] message authentication codes (MACs), [20][21][22][23] etc, [24][25][26] were broken by different quantum algorithms, including Simon algorithm, [27] Grover algorithm, [28] Grover-meets-Simon algorithm, [19] Bernstein-Vazirani (BV) algorithm, [29] etc.…”

Analysis of Data Tenure Field and Regulatory Logic in the Internet Era

“…In the total flow of the AES algorithm, three substitutions and one column mixing operation are included, which are carried out reciprocally using byte substitution, row shifting, column mixing, and round key addition, and a total of nine rounds of iterations are completed, where the tenth round of iterations does not include column mixing [14]. In the final session, the round key addition is employed to process the data and generate the ciphertext.…”

Application of Big Data Analysis and Intelligent Algorithm in Power System Operation Optimization

“…A quantum critical generation method based on R = 1 M bit/s is proposed. Packets queued for encryption obey Poisson distribution, and the arrival rate of packets queued for encryption is the same [14]. The total requirement for the four queue keys is 1M bit/s.…”