In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful: if the secret key is (i) uniquely determined by a small number of plaintext-ciphertext pairs, (ii) the block cipher can be evaluated efficiently, and (iii) a superposition of related keys can be queried, then the key can be extracted efficiently.
In a basic related-key attack against a block cipher, the adversary has access to encryptions under keys that differ from the target key by bit-flips. In this short note we show that for a quantum adversary such attacks are quite powerful: if the secret key is (i) uniquely determined by a small number of plaintext-ciphertext pairs, (ii) the block cipher can be evaluated efficiently, and (iii) a superposition of related keys can be queried, then the key can be extracted efficiently.
Due to the powerful computing capability of quantum computers, cryptographic researchers have applied quantum algorithms to cryptanalysis and obtained many interesting results in recent years. In this paper, we study related-key attack in the quantum setting, and proposed a specific related-key attack which can recover the key of block ciphers efficiently, as long as the attacked block ciphers satisfy certain conditions. The attack algorithm employs Bernstein-Vazirani algorithm as a subroutine and requires the attacker to query the encryption oracle with quantum superpositions. Afterwards, we rigorously demonstrate the validity of the attack and analyze its complexity. Our work shows that related-key attack is quite powerful when combined with quantum algorithms, and provides some guidance for the design of block ciphers that are secure against quantum adversaries.
It has been said that security of symmetric key schemes is not so much affected by quantum computers, compared to public key schemes. However, recent works revealed that, in some specific situations, symmetric key schemes are also broken in polynomial time by adversaries with quantum computers. These works contain a quantum distinguishing attack on 3-round Feistel ciphers and a quantum key recovery attack on the Even-Mansour cipher by Kuwakado and Morii, in addition to the quantum forgery attack on CBC-MAC which is proposed independently by Kaplan et al., and by Santoli and Schaffner. Iterated Even-Mansour cipher is a simple but important block cipher, which can be regarded as an idealization of AES. Whether there exists an efficient quantum algorithm that can break iterated Even-Mansour cipher with independent subkeys is an important problem from the viewpoint of analyzing post-quantum security of block ciphers. Actually there is an efficient quantum attack on iterated Even-Mansour cipher by Kaplan et al., but their attack can only be applied in the case that all subkeys are the same. This paper shows that there is a polynomial time quantum algorithm that recovers partial keys of the iterated Even-Mansour cipher with independent subkeys, in a related-key setting. The related-key condition is somewhat strong, but our algorithm can recover subkeys with two related oracles. In addition, we also show that our algorithm can recover all keys of the i-round iterated Even-Mansour cipher, if we are allowed to access i related quantum oracles. To realize quantum related-key attacks, we extend Simon's quantum algorithm so that we can recover the hidden period of a function that is periodic only up to constant. Our technique is to take differential of the target function to make a double periodic function, and then apply Simon's algorithm.
Recent results on quantum cryptanalysis show that some symmetric key schemes can be broken in polynomial time even if they are proven to be secure in the classical setting. Liskov, Rivest, and Wagner showed that secure tweakable block ciphers can be constructed from secure block ciphers in the classical setting. However, Kaplan et al. showed that their scheme can be broken by polynomial time quantum superposition attacks, even if underlying block ciphers are quantum-secure. Since then, it remains open if there exists a mode of block ciphers to build quantum-secure tweakable block ciphers. This paper settles the problem in the reduction-based provable security paradigm. We show the first design of quantum-secure tweakable block ciphers based on quantum-secure block ciphers, and present a provable security bound. Our construction is simple, and when instantiated with a quantum-secure n-bit block cipher, it is secure against attacks that query arbitrary quantum superpositions of plaintexts and tweaks up to O(2n/6) quantum queries. Our security proofs use the compressed oracle technique introduced by Zhandry. More precisely, we use an alternative formalization of the technique introduced by Hosoyamada and Iwata.
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.
Abstract In practice today, quantum keys are often reused because of practical limitations. It is clear that reusing a key weakens security compared to one-time-pad encryption, where perfect secrecy is achieved. For this reason, it is important to understand how the effort needed to find the key changes when the key is reused. We use the trace distance between two quantum states as a measure of closeness. Its maximum value is one, which means the two states are as different as possible. With simple arguments, we show that the trace distance is bounded above by several terms that capture (i) non-ideal quantum keys, (ii) plaintext redundancy, (iii) the number of key reuses, and (iv) the number of collisions of the block cipher. The trace distance approaches one exponentially fast with plaintext redundancy and with the number of key reuses; this means brute-force search becomes as easy as possible. For a random block cipher, the expected trace distance grows linearly with the number of key uses, with coefficient e −1 ( e is Euler’s constant). The result is information-theoretic in nature.
The development of quantum computers represents an important advancement in computing, using quantum mechanics to address problems that were previously difficult to solve. This technological advancement poses a challenge for cryptographic systems. While some methods are known to be vulnerable, the impact of quantum computing on symmetric cryptography has received less research attention, largely because the common advice is to simply double the key size. This paper explores how quantum computing affects symmetric cryptography, focusing on block cipher-based cryptography. It surveys existing literature on the quantum resilience of symmetric cryptographic primitives based on block ciphers and their security in various scenarios. Not all symmetric cryptographic functionalities are quantum-secure, and their security depends on the specific adversary model being considered. We provide an overview of the research conducted and pinpoint areas where further investigation is needed.