Abstract Similar to the classical meet-in-the-middle algorithm, the storage and computation complexity are the key factors that decide the efficiency of the quantum meet-in-the-middle algorithm. Aiming at the target vector of fixed weight, based on the quantum meet-in-the-middle algorithm, the algorithm for searching all n-product vectors with the same weight is presented, whose complexity is better than the exhaustive search algorithm. And the algorithm can reduce the storage complexity of the quantum meet-in-the-middle search algorithm. Then based on the algorithm and the knapsack vector of the Chor-Rivest public-key crypto of fixed weight d, we present a general quantum meet-in-the-middle search algorithm based on the target solution of fixed weight, whose computational complexity is ∑ j = 0 d ( O ( C n - k + 1 d - j ) + O ( C k j log C k j ) ) with Σ d i =0 C k i memory cost. And the optimal value of k is given. Compared to the quantum meet-in-the-middle search algorithm for knapsack problem and the quantum algorithm for searching a target solution of fixed weight, the computational complexity of the algorithm is lower. And its storage complexity is smaller than the quantum meet-in-the-middle-algorithm.
To enhance the efficiency of the quantum differential Meet-In-The-Middle attack, an improved scheme based on quantum collision search is proposed. The traditional quantum search steps were replaced with Ambainis’ quantum collision search algorithm. This replacement optimized the matching process between candidate keys and plaintexts in the Meet-in-the-Middle phase and significantly reduced time complexity. The improved attack scheme is applied to PIPO-128, SKINNY-128-384, and AES-256, achieving key recovery attacks for 8, 23, and 12 rounds, respectively. Analysis results under both Q1 and Q2 models demonstrate that the proposed scheme outperforms existing classical and quantum attacks in both time and memory complexity, validating its effectiveness and superiority in cryptanalysis.
Abstract At CRYPTO 2023, Boura et al. proposed a new cryptanalysis technique, differential meet‐in‐the‐middle (MITM) attack. They used MITM technique to make the key recovery step of a differential attack more efficient. In this study, a quantum differential meet‐in‐the‐middle attack is proposed by using nested quantum search algorithm, which can achieve up to a quadratic speed‐up compared to the classical version. Besides, the time complexity of the attack can be reduced by at least a factor of ( is the guessed key length and is the block size) compared to the first quantum differential attack proposed by Kaplan et al. at ToSC 2016. Finally, to demonstrate the efficiency of our attack, it is applied to two reduced‐round lightweight block ciphers, PIPO and SIMON , to evaluate their post‐quantum security. When attacking the same number of rounds, the time complexity of our attack is significantly lower than that of classical attacks. For the 8‐round PIPO‐128 , the attack significantly improves efficiency, reducing the time complexity from to , cutting down the required qRAM size by a factor of and obtaining the data complexity instead of compared to the best quantum attack proposed by Schrottenloher at CRYPTO 2023. For the 19‐round SIMON‐32‐64 , the time complexity here will be instead of compared to the other quantum attack, and the attack can target more rounds than using Grover‐meets‐Simon technique.
NTRU is one of the most widely used public-key cryptosystems and its security has been an active research topic. This paper proposes a new way to find NTRU-2005 private key. The algorithm is based on meet-in-the-middle attack and a quantum algorithm for searching the fixed weight target. Compared with the current classical and quantum meet-in-the-middle attacks, our algorithm has lower time and space complexity. Moreover, this attack can also be applied against different versions of NTRU. The result can help to understand the security of NTRU better.
Key-length extension (KLE) techniques provide a general approach to enhancing the security of block ciphers by using longer keys. There are mainly two classes of KLE techniques, cascade encryption and XOR-cascade encryption. This paper presents several quantum meet-in-the-middle (MITM) attacks against two specific KLE constructions.
For the two-key triple encryption (2kTE), we propose two quantum MITM attacks under the Q2 model. The first attack, leveraging the quantum claw-finding (QCF) algorithm, achieves a time complexity of
O(22κ/3) with
O(22κ/3) quantum random access memory (QRAM). The second attack, based on Grover's algorithm, achieves a time complexity of
O(2κ/2) with
O(2κ) QRAM. The latter complexity is nearly identical to Grover-based brute-force attack on the underlying block cipher, indicating that 2kTE does not enhance security under the Q2 model when sufficient QRAM resources are available.
For the 3XOR-cascade encryption (3XCE), we propose a quantum MITM attack applicable to the Q1 model. This attack requires no QRAM and has a time complexity of
O(2(κ+n)/2) (
κ and
n are the key length and block length of the underlying block cipher, respectively.), achieving a quadratic speedup over classical MITM attack.
Furthermore, we extend the quantum MITM attack to quantum sieve-in-the-middle (SITM) attack, which is applicable for more constructions. We present a general quantum SITM framework for the construction
ELE=E2∘L∘E1 and provide specific attack schemes for three different forms of the middle layer
L. The quantum SITM attack technique can be further applied to a broader range of quantum cryptanalysis scenarios.
Abstract Quantum Algorithms reduce the computational complexity or solve certain difficult problems that were originally impossible to solve with classical computers. Grover's search algorithm is a Quantum computation algorithm that can find target elements from a set of unstructured data with the best possible, O(√ N) queries. Grover's search Quantum circuits implemented accurately can be used to successfully search and find the keys of Symmetric ciphers. However, very few demonstrations of such practical cryptanalysis are available. In this paper, practical Quantum cryptanalysis circuits for Affine Cipher are proposed and demonstrated, that successfully break the cipher by finding the keys.