Finding Hash Collisions with Quantum Computers by Using Differential Trails with Smaller Probability than Birthday Bound

In this paper we spot light on dedicated quantum collision attacks on concrete hash functions, which has not received much attention so far. In the classical setting, the generic complexity to find collisions of an $n$-bit hash function is $O(2^{n/2})$, thus classical collision attacks based on differential cryptanalysis such as rebound attacks build differential trails with probability higher than $2^{-n/2}$. By the same analogy, generic quantum algorithms such as the BHT algorithm find collisions with complexity $O(2^{n/3})$. With quantum algorithms, a pair of messages satisfying a differential trail with probability $p$ can be generated with complexity $p^{-1/2}$. Hence, in the quantum setting, some differential trails with probability up to $2^{-2n/3}$ that cannot be exploited in the classical setting may be exploited to mount a collision attack in the quantum setting. In particular, the number of attacked rounds may increase. In this paper, we attack two international hash function standards: AES-MMO and Whirlpool. For AES-MMO, we present a $7$-round differential trail with probability $2^{-80}$ and use it to find collisions with a quantum version of the rebound attack, while only $6$ rounds can be attacked in the classical setting. For Whirlpool, we mount a collision attack based on a $6$-round differential trail from a classical rebound distinguisher with a complexity higher than the birthday bound. This improves the best classical attack on 5 rounds by 1. We also show that those trails are optimal in our approach. Our results have two important implications. First, there seems to exist a common belief that classically secure hash functions will remain secure against quantum adversaries. Indeed, several second-round candidates in the NIST post-quantum competition use existing hash functions, say SHA-3, as quantum secure ones. Our results disprove this common belief. Second, our observation suggests that differential trail search should not stop with probability $2^{-n/2}$ but should consider up to $2^{-2n/3}$. Hence it deserves to revisit the previous differential trail search activities

Internal symmetries and linear properties: Full-permutation distinguishers and improved collisions on Gimli

Gimli is a family of cryptographic primitives (both a hash function and an AEAD scheme) that has been selected for the second round of the NIST competition for standardizing new lightweight designs. The candidate Gimli is based on the permutation Gimli, which was presented at CHES 2017. In this paper, we study the security of both the permutation and the constructions that are based on it. We exploit the slow diffusion in Gimli and its internal symmetries to build, for the first time, a distinguisher on the full permutation of complexity 2^64. We also provide a practical distinguisher on 23 out of the full 24 rounds of Gimli that has been implemented. Next, we give (full state) collision and semi-free start collision attacks on Gimli-Hash, reaching, respectively, up to 12 and 18 rounds. On the practical side, we compute a collision on 8-round Gimli-Hash. In the quantum setting, these attacks reach 2 more rounds. Finally, we perform the first study of linear trails in Gimli, and we find a linear distinguisher on the full permutation

Internal Symmetries and Linear Properties: Full-permutation Distinguishers and Improved Collisions on Gimli

International audienceGimli is a family of cryptographic primitives (both a hash function and an AEAD scheme) that has been selected for the second round of the NIST competition for standardizing new lightweight designs. The candidate Gimli is based on the permutation Gimli, which was presented at CHES 2017. In this paper, we study the security of both the permutation and the constructions that are based on it. We exploit the slow diffusion in Gimli and its internal symmetries to build, for the first time, a distinguisher on the full permutation of complexity 2 64. We also provide a practical distinguisher on 23 out of the full 24 rounds of Gimli that has been implemented. Next, we give (full state) collision and semi-free-start collision attacks on Gimli-Hash, reaching respectively up to 12 and 18 rounds. On the practical side, we compute a collision on 8-round Gimli-Hash. In the quantum setting, these attacks reach 2 more rounds. Finally, we perform the first study of linear trails in Gimli, and we find a linear distinguisher on the full permutation

New results on Gimli: full-permutation distinguishers and improved collisions

International audienceGimli is a family of cryptographic primitives (both a hash function and an AEAD scheme) that has been selected for the second round of the NIST competition for standardizing new lightweight designs. The candidate Gimli is based on the permutation Gimli, which was presented at CHES 2017. In this paper, we study the security of both the permutation and the constructions that are based on it. We exploit the slow diffusion in Gimli and its internal symmetries to build, for the first time, a distinguisher on the full permutation of complexity 2 64. We also provide a practical distinguisher on 23 out of the full 24 rounds of Gimli that has been implemented. Next, we give (full state) collision and semi-free-start collision attacks on Gimli-Hash, reaching respectively up to 12 and 18 rounds. On the practical side, we compute a collision on 8-round Gimli-Hash. In the quantum setting, these attacks reach 2 more rounds. Finally, we perform the first study of linear trails in the permutation, and we propose differential-linear cryptanalysis that reach up to 17 rounds of Gimli

Quantum Rebound Attacks on Reduced-Round ARIA-Based Hash Functions

ARIA is a block cipher proposed by Kwon et al. at ICISC 2003, and it is widely used as the national standard block cipher in the Republic of Korea. In this study, we identify some flaws in the quantum rebound attack on 7-round ARIA-DM proposed by Dou et al., and we reveal that the limit of this attack is up to 5-round. Our revised attack applies not only to ARIA-DM but also to ARIA-MMO and ARIA-MP among the PGV models, and it is valid for all key lengths of ARIA. Moreover, we present dedicated quantum rebound attacks on 7-round ARIA-Hirose and ARIA-MJH for the first time. These attacks are only valid for the 256-bit key length of ARIA because they are constructed using the degrees of freedom in the key schedule. All our attacks are faster than the generic quantum attack in the cost metric of time–space tradeoff

Saturnin: a suite of lightweight symmetric algorithms for post-quantum security

Soumission à la compétition "Lightweight Cryptography" du NISTThe cryptographic algorithms needed to ensure the security of our communications have a cost. For devices with little computing power, whose number is expected to grow significantly with the spread of the Internet of Things (IoT), this cost can be a problem. A simple answer to this problem is a compromise on the security level: through a weaker round function or a smaller number of rounds, the security level can be decreased in order to cheapen the implementation of the cipher. At the same time, quantum computers are expected to disrupt the state of the art in cryptography in the near future. For public key cryptography, the NIST has organized a dedicated process to standardize new algorithms. The impact of quantum computing is harder to assess in the symmetric case but its study is an active research area. In this document, we specify a new block cipher, Saturnin, and its usage in different modes to provide hashing and authenticated encryption in such a way that we can rigorously argue its security in the post-quantum setting. Its security analysis follows naturally from that of the AES, while our use of components that are easily implemented in a bitsliced fashion ensures a low cost for our primitives. Our aim is to provide a new lightweight suite of algorithms that performs well on small devices, in particular micro-controllers, while providing a high security level even in the presence of quantum computers. Saturnin is a 256-bit block cipher with a 256-bit key and an additional 9-bit parameter for domain separation. Using it, we built two authenticated ciphers and a hash function. • Saturnin-CTR-Cascade is an authenticated cipher using the counter mode and a separate MAC. It requires two passes over the data but its implementation does not require the inverse block cipher. • Saturnin-Short is an authenticated cipher intended for messages with a length strictly smaller than 128 bits which uses only one call to Saturnin to provide confidentiality and integrity. • Saturnin-Hash is a 256-bit hash function. In this document, we specify this suite of algorithms and argue about their security in both the classical and the post-quantum setting

Rebound Attacks on SKINNY Hashing with Automatic Tools

In ToSC\u2720, a new approach combining Mix-Integer Linear Programming (MILP) tool and Constraint Programming (CP) tool to search for boomerang distinguishers is proposed and later used for rebound attack in ASIACRYPT\u2721 and CRYPTO\u2722. In this work, we extend these techniques to mount collision attacks on SKINNY-128-256 MMO hashing mode in classical and quantum settings. The first results of 17-round (and 15-round) free-start collision attack on this variant of SKINNY hashing mode are presented. Moreover, one more round of the inbound phase is covered leading to the best existing classical free-start collision attack of 19-round on the SKINNY-128-384 MMO hashing

Exploring SAT for Cryptanalysis: (Quantum) Collision Attacks against 6-Round SHA-3 (Full Version)

In this work, we focus on collision attacks against instances of SHA-3 hash family in both classical and quantum settings. Since the 5-round collision attacks on SHA3-256 and other variants proposed by Guo et al. at JoC~2020, no other essential progress has been published. With a thorough investigation, we identify that the challenges of extending such collision attacks on SHA-3 to more rounds lie in the inefficiency of differential trail search. To overcome this obstacle, we develop a SAT-based automatic search toolkit. The tool is used in multiple intermediate steps of the collision attacks and exhibits surprisingly high efficiency in differential trail search and other optimization problems encountered in the process. As a result, we present the first 6-round classical collision attack on SHAKE-128 with time complexity $2^{123.5}$, which also forms a quantum collision attack with quantum time ${{2^{67.25}}/{\sqrt{S}}}$, and the first 6-round quantum collision attack on SHA3-224 and SHA3-256 with quantum time ${{2^{97.75}}/{\sqrt{S}}}$ and ${{2^{104.25}}/{\sqrt{S}}}$, both with negligible requirement of classical and quantum memory. The fact that classical collision attacks do not apply to 6-round SHA3-224 and SHA3-256 shows the higher coverage of quantum collision attacks, which is consistent with that on SHA-2 observed by Hosoyamada and Sasaki at CRYPTO~2021

Saturnin: a suite of lightweight symmetric algorithms for post-quantum security

International audienceThe cryptographic algorithms needed to ensure the security of our communications have a cost. For devices with little computing power, whose number is expected to grow significantly with the spread of the Internet of Things (IoT), this cost can be a problem. A simple answer to this problem is a compromise on the security level: through a weaker round function or a smaller number of rounds, the security level can be decreased in order to cheapen the implementation of the cipher. At the same time, quantum computers are expected to disrupt the state of the art in cryptography in the near future. For public-key cryptography, the NIST has organized a dedicated process to standardize new algorithms. The impact of quantum computing is harder to assess in the symmetric case but its study is an active research area.In this paper, we specify a new block cipher, Saturnin, and its usage in different modes to provide hashing and authenticated encryption in such a way that we can rigorously argue its security in the post-quantum setting. Its security analysis follows naturally from that of the AES, while our use of components that are easily implemented in a bitsliced fashion ensures a low cost for our primitives. Our aim is to provide a new lightweight suite of algorithms that performs well on small devices, in particular micro-controllers, while providing a high security level even in the presence of quantum computers. Saturnin is a 256-bit block cipher with a 256-bit key and an additional 9-bit parameter for domain separation. Using it, we built two authenticated ciphers and a hash function.• Saturnin-CTR-Cascade is an authenticated cipher using the counter mode and a separate MAC. It requires two passes over the data but its implementation does not require the inverse block cipher.• Saturnin-Short is an authenticated cipher intended for messages with a length strictly smaller than 128 bits which uses only one call to Saturnin to providenconfidentiality and integrity.• Saturnin-Hash is a 256-bit hash function.In this paper, we specify this suite of algorithms and argue about their security in both the classical and the post-quantum setting

Quantum Collision Attacks on AES-like Hashing with Low Quantum Random Access Memories

At EUROCRYPT 2020, Hosoyamada and Sasaki proposed the first dedicated quantum attack on hash functions --- a quantum version of the rebound attack exploiting differentials whose probabilities are too low to be useful in the classical setting. This work opens up a new perspective toward the security of hash functions against quantum attacks. In particular, it tells us that the search for differentials should not stop at the classical birthday bound. Despite these interesting and promising implications, the concrete attacks described by Hosoyamada and Sasaki make use of large quantum random access memories (qRAMs), a resource whose availability in the foreseeable future is controversial even in the quantum computation community. Without large qRAMs, these attacks incur significant increases in time complexities. In this work, we reduce or even avoid the use of qRAMs by performing a quantum rebound attack based on differentials with non-full-active super S-boxes. Along the way, an MILP-based method is proposed to systematically explore the search space of useful truncated differentials with respect to rebound attacks. As a result, we obtain improved attacks on AES-MMO, AES-MP, and the first classical collision attacks on 4- and 5-round Grostl-512. Interestingly, the use of non-full-active super S-box differentials in the analysis of AES-MMO gives rise to new difficulties in collecting enough starting points. To overcome this issue, we consider attacks involving two message blocks to gain more degrees of freedom, and we successfully compress the qRAM demand of the collision attacks on AES-MMO and AES-MP (EUROCRYPT 2020) from $2^{48}$ to a range from $2^{16}$ to $0$, while still maintaining a comparable time complexity. To the best of our knowledge, these are the first dedicated quantum attacks on hash functions that slightly outperform Chailloux, Naya-Plasencia, and Schrottenloher\u27s generic quantum collision attack (ASIACRYPT 2017) in a model where large qRAMs are not available. This work demonstrates again how a clever combination of classical cryptanalytic technique and quantum computation leads to improved attacks, and shows that the direction pointed out by Hosoyamada and Sasaki deserves further investigation