Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.303-340
R. Makarim, R. Rohit
Being one of the winners of the CAESAR competition and a finalist of the ongoing NIST lightweight cryptography competition, the authenticated encryption with associated data algorithm Ascon has withstood extensive security evaluation. Despite the substantial cryptanalysis, the tightness on Ascon’s differential bounds is still not well-understood until very recently, at ToSC 2022, Erlacher et al. have proven lower bounds (not tight) on the number of differential and linear active Sboxes for 4 and 6 rounds. However, a tight bound for the minimum number of active Sboxes for 4 − 6 rounds is still not known.In this paper, we take a step towards solving the above tightness problem by efficiently utilizing both Satisfiability Modulo Theories (SMT) and Mixed Integer Linear Programming (MILP) based automated tools. Our first major contribution (using SMT) is the set of all valid configurations of active Sboxes (for e.g., 1, 3 and 11 active Sboxes at round 0, 1 and 2, respectively) up to 22 active Sboxes and partial sets for 23 to 32 active Sboxes for 3-round differential trails. We then prove that the weight (differential probability) of any 3-round differential trail is at least 40 by finding the minimum weights (using MILP) corresponding to each configuration till 19 active Sboxes. As a second contribution, for 4 rounds, we provide several necessary conditions (by extending 3 round trails) which may result in a differential trail with at most 44 active Sboxes. We find 5 new configurations for 44 active Sboxes and show that in total there are 9289 cases to check for feasibility in order to obtain the actual lower bound for 4 rounds. We also provide an estimate of the time complexity to solve these cases. Our third main contribution is the improvement in the 7-year old upper bound on active Sboxes for 4 and 5 rounds from 44 to 43 and from 78 to 72, respectively. Moreover, as a direct application of our approach, we find new 4-round linear trails with 43 active Sboxes and also a 5-round linear trail with squared correlation 2−184 while the previous best known linear trail has squared correlation 2−186. Finally, we provide the implementations of our SMT and MILP models, and actual trails to verify the correctness of results.
{"title":"Towards Tight Differential Bounds of Ascon A Hybrid Usage of SMT and MILP","authors":"R. Makarim, R. Rohit","doi":"10.46586/tosc.v2022.i3.303-340","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.303-340","url":null,"abstract":"Being one of the winners of the CAESAR competition and a finalist of the ongoing NIST lightweight cryptography competition, the authenticated encryption with associated data algorithm Ascon has withstood extensive security evaluation. Despite the substantial cryptanalysis, the tightness on Ascon’s differential bounds is still not well-understood until very recently, at ToSC 2022, Erlacher et al. have proven lower bounds (not tight) on the number of differential and linear active Sboxes for 4 and 6 rounds. However, a tight bound for the minimum number of active Sboxes for 4 − 6 rounds is still not known.In this paper, we take a step towards solving the above tightness problem by efficiently utilizing both Satisfiability Modulo Theories (SMT) and Mixed Integer Linear Programming (MILP) based automated tools. Our first major contribution (using SMT) is the set of all valid configurations of active Sboxes (for e.g., 1, 3 and 11 active Sboxes at round 0, 1 and 2, respectively) up to 22 active Sboxes and partial sets for 23 to 32 active Sboxes for 3-round differential trails. We then prove that the weight (differential probability) of any 3-round differential trail is at least 40 by finding the minimum weights (using MILP) corresponding to each configuration till 19 active Sboxes. As a second contribution, for 4 rounds, we provide several necessary conditions (by extending 3 round trails) which may result in a differential trail with at most 44 active Sboxes. We find 5 new configurations for 44 active Sboxes and show that in total there are 9289 cases to check for feasibility in order to obtain the actual lower bound for 4 rounds. We also provide an estimate of the time complexity to solve these cases. Our third main contribution is the improvement in the 7-year old upper bound on active Sboxes for 4 and 5 rounds from 44 to 43 and from 78 to 72, respectively. Moreover, as a direct application of our approach, we find new 4-round linear trails with 43 active Sboxes and also a 5-round linear trail with squared correlation 2−184 while the previous best known linear trail has squared correlation 2−186. Finally, we provide the implementations of our SMT and MILP models, and actual trails to verify the correctness of results.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"28 1","pages":"303-340"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85153243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.191-216
T. Johansson, W. Meier, Vu Nguyen
Firekite is a synchronous stream cipher using a pseudo-random number generator (PRNG) whose security is conjectured to rely on the hardness of the Learning Parity with Noise (LPN) problem. It is one of a few LPN-based symmetric encryption schemes, and it can be very efficiently implemented on a low-end SoC FPGA. The designers, Bogos, Korolija, Locher and Vaudenay, demonstrated appealing properties of Firekite, such as requiring only one source of cryptographically strong bits, small key size, high attainable throughput, and an estimate for the bit level security depending on the selected practical parameters.We propose distinguishing and key-recovery attacks on Firekite by exploiting the structural properties of its PRNG. We adopt several birthday-paradox techniques to show that a particular sum of Firekite’s output has a low Hamming weight with higher probability than the random case. We achieve the best distinguishing attacks with complexities 266.75 and 2106.75 for Firekite’s parameters corresponding to 80-bit and 128-bit security, respectively. By applying the distinguishing attacks and an additional algorithm we describe, one can also recover the secret matrix used in the Firekite PRNG, which is built from the secret key bits. This key recovery attack works on most large instances of Firekite parameters and has slightly larger complexity, for instance, 269.87 on the 80-bit security parameters n = 16,384, m = 216, k = 216.
Firekite是一种使用伪随机数生成器(PRNG)的同步流密码，其安全性被推测依赖于带噪声的学习奇偶性(LPN)问题的硬度。它是为数不多的基于lpn的对称加密方案之一，可以非常有效地在低端SoC FPGA上实现。设计师Bogos, Korolija, Locher和Vaudenay展示了Firekite的吸引人的特性，例如只需要一个加密强比特源，密钥大小小，可实现的吞吐量高，以及根据所选的实际参数估计比特级安全性。我们利用Firekite的PRNG结构特性，提出了针对Firekite的识别和密钥恢复攻击。我们采用了几种生日悖论技术来证明Firekite输出的特定总和具有比随机情况更高的概率的低汉明权值。我们对Firekite的80位和128位安全参数分别实现了复杂度为266.75和2106.75的最佳区分攻击。通过应用我们描述的区分攻击和附加算法，还可以恢复Firekite PRNG中使用的秘密矩阵，该矩阵是由秘密密钥位构建的。这种密钥恢复攻击适用于Firekite参数的大多数大型实例，并且具有稍大的复杂性，例如，对80位安全参数n = 16,384, m = 216, k = 216进行269.87攻击。
{"title":"Attacks on the Firekite cipher","authors":"T. Johansson, W. Meier, Vu Nguyen","doi":"10.46586/tosc.v2022.i3.191-216","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.191-216","url":null,"abstract":"Firekite is a synchronous stream cipher using a pseudo-random number generator (PRNG) whose security is conjectured to rely on the hardness of the Learning Parity with Noise (LPN) problem. It is one of a few LPN-based symmetric encryption schemes, and it can be very efficiently implemented on a low-end SoC FPGA. The designers, Bogos, Korolija, Locher and Vaudenay, demonstrated appealing properties of Firekite, such as requiring only one source of cryptographically strong bits, small key size, high attainable throughput, and an estimate for the bit level security depending on the selected practical parameters.We propose distinguishing and key-recovery attacks on Firekite by exploiting the structural properties of its PRNG. We adopt several birthday-paradox techniques to show that a particular sum of Firekite’s output has a low Hamming weight with higher probability than the random case. We achieve the best distinguishing attacks with complexities 266.75 and 2106.75 for Firekite’s parameters corresponding to 80-bit and 128-bit security, respectively. By applying the distinguishing attacks and an additional algorithm we describe, one can also recover the secret matrix used in the Firekite PRNG, which is built from the secret key bits. This key recovery attack works on most large instances of Firekite parameters and has slightly larger complexity, for instance, 269.87 on the 80-bit security parameters n = 16,384, m = 216, k = 216.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"84 1","pages":"191-216"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74934056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
ZUC-256 is a stream cipher designed for 5G applications by the ZUC team. Together with AES-256 and SNOW-V, it is currently being under evaluation for standardized algorithms in 5G mobile telecommunications by Security Algorithms Group of Experts (SAGE). A notable feature of the round update function of ZUC-256 is that many operations are defined over different fields, which significantly increases the difficulty to analyze the algorithm.As a main contribution, with the tools of the modular difference, signed difference and XOR difference, we develop new techniques to carefully control the interactions between these operations defined over different fields. At first glance, our techniques are somewhat similar to those developed by Wang et al. for the MD-SHA hash family. However, as ZUC-256 is quite different from the MD-SHA hash family and its round function is much more complex, we are indeed dealing with different problems and overcoming new obstacles.As main results, by utilizing complex input differences, we can present the first distinguishing attacks on 31 out of 33 rounds of ZUC-256 and 30 out of 33 rounds of the new version of ZUC-256 called ZUC-256-v2 with low time and data complexities, respectively. These attacks target the initialization phase and work in the related-key model with weak keys. Moreover, with a novel IV-correcting technique, we show how to efficiently recover at least 16 key bits for 15-round ZUC-256 and 14-round ZUC-256-v2 in the related-key setting, respectively. It is unpredictable whether our attacks can be further extended to more rounds with more advanced techniques. Based on the current attacks, we believe that the full 33 initialization rounds provide marginal security.
{"title":"New Cryptanalysis of ZUC-256 Initialization Using Modular Differences","authors":"Fukang Liu, W. Meier, Santanu Sarkar, Gaoli Wang, Ryoma Ito, Takanori Isobe","doi":"10.46586/tosc.v2022.i3.152-190","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.152-190","url":null,"abstract":"ZUC-256 is a stream cipher designed for 5G applications by the ZUC team. Together with AES-256 and SNOW-V, it is currently being under evaluation for standardized algorithms in 5G mobile telecommunications by Security Algorithms Group of Experts (SAGE). A notable feature of the round update function of ZUC-256 is that many operations are defined over different fields, which significantly increases the difficulty to analyze the algorithm.As a main contribution, with the tools of the modular difference, signed difference and XOR difference, we develop new techniques to carefully control the interactions between these operations defined over different fields. At first glance, our techniques are somewhat similar to those developed by Wang et al. for the MD-SHA hash family. However, as ZUC-256 is quite different from the MD-SHA hash family and its round function is much more complex, we are indeed dealing with different problems and overcoming new obstacles.As main results, by utilizing complex input differences, we can present the first distinguishing attacks on 31 out of 33 rounds of ZUC-256 and 30 out of 33 rounds of the new version of ZUC-256 called ZUC-256-v2 with low time and data complexities, respectively. These attacks target the initialization phase and work in the related-key model with weak keys. Moreover, with a novel IV-correcting technique, we show how to efficiently recover at least 16 key bits for 15-round ZUC-256 and 14-round ZUC-256-v2 in the related-key setting, respectively. It is unpredictable whether our attacks can be further extended to more rounds with more advanced techniques. Based on the current attacks, we believe that the full 33 initialization rounds provide marginal security.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"12 1","pages":"152-190"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76881010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.1-19
G. Brian, Antonio Faonio, João L. Ribeiro, D. Venturi
We construct non-malleable codes in the split-state model with codeword length m + 3λ or m + 5λ, where m is the message size and λ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a distribution with sufficient min-entropy, even under related-key attacks with respect to an arbitrary but fixed key relation. Importantly, indistinguishability only holds with respect to the original secret key (and not with respect to the tampered secret key).In a previous work, Fehr, Karpman, and Mennink (ToSC 2018) used a related assumption (where the block cipher inputs can be chosen by the adversary, and where indistinguishability holds even with respect to the tampered key) to construct a nonmalleable code in the split-state model with codeword length m + 2λ. Unfortunately, no block cipher (even an ideal one) satisfies their assumption when the tampering function is allowed to be cipher-dependent. In contrast, we are able to show that entropic fixed-related-key security holds in the ideal cipher model with respect to a large class of cipher-dependent tampering attacks (including those which break the assumption of Fehr, Karpman, and Mennink).
{"title":"Short Non-Malleable Codes from Related-Key Secure Block Ciphers, Revisited","authors":"G. Brian, Antonio Faonio, João L. Ribeiro, D. Venturi","doi":"10.46586/tosc.v2022.i3.1-19","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.1-19","url":null,"abstract":"We construct non-malleable codes in the split-state model with codeword length m + 3λ or m + 5λ, where m is the message size and λ is the security parameter, depending on how conservative one is. Our scheme is very simple and involves a single call to a block cipher meeting a new security notion which we dub entropic fixed-related-key security, which essentially means that the block cipher behaves like a pseudorandom permutation when queried upon inputs sampled from a distribution with sufficient min-entropy, even under related-key attacks with respect to an arbitrary but fixed key relation. Importantly, indistinguishability only holds with respect to the original secret key (and not with respect to the tampered secret key).In a previous work, Fehr, Karpman, and Mennink (ToSC 2018) used a related assumption (where the block cipher inputs can be chosen by the adversary, and where indistinguishability holds even with respect to the tampered key) to construct a nonmalleable code in the split-state model with codeword length m + 2λ. Unfortunately, no block cipher (even an ideal one) satisfies their assumption when the tampering function is allowed to be cipher-dependent. In contrast, we are able to show that entropic fixed-related-key security holds in the ideal cipher model with respect to a large class of cipher-dependent tampering attacks (including those which break the assumption of Fehr, Karpman, and Mennink).","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"29 1","pages":"1-19"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90582030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.20-72
Lorenzo Grassi, Silvia Onofri, M. Pedicini, Luca Sozzi
Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over Fp for a large prime p have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps x↦xd. In this paper, we start an analysis of new non-linear permutation functions over Fnp that can be used as building blocks in such symmetrickey primitives. Given a local map F : Fmp→ Fp, we limit ourselves to focus on S-Boxes over Fnp for n ≥ m defined as SF (x0, x1, . . . , xn−1) = y0|y1| . . . |yn−1 where yi := F(xi, xi+1, . . . , xi+m−1). As main results, we prove that• given any quadratic function F : F2p→ Fp, the corresponding S-Box SF over Fnp for n ≥ 3 is never invertible;• similarly, given any quadratic function F : F3p → Fp, the corresponding S-Box SF over Fnp for n ≥ 5 is never invertible.Moreover, for each p ≥ 3, we present (1st) generalizations of the Lai-Massey construction over Fnp defined as before via functions F : Fmp → Fp for each n = m ≥ 2 and (2nd) (non-trivial) quadratic functions F : F3p → Fp such that SF over Fnp for n ∈ {3, 4} is invertible. As an open problem for future work, we conjecture that for each m ≥ 1 there exists a finite integer nmax(m) such that SF over Fnp defined as before via a quadratic function F : Fmp →Fp is not invertible for each n ≥ nmax(m). Finally, as a concrete application, we propose Neptune, a variant of the sponge hash function Poseidon, whose non-linear layer is designed by taking into account the results presented in this paper. We show that this variant leads to a concrete multiplication reduction with respect to Poseidon.
在诸如安全多方计算(MPC)、完全同态加密(FHE)和零知识证明(ZK)等新应用的推动下，最近在文献中提出了许多MPC、FHE和ZK友好的对称密钥原语，这些原语可以最大限度地减少大素数p在Fp上的乘法次数。这个目标通常是通过幂映射x x xd实例化非线性层来实现的。在本文中，我们开始分析Fnp上的新的非线性排列函数，这些函数可以用作这种对称基元的构建块。给定一个局部映射F: Fmp→Fp，我们限制自己关注Fnp上n≥m的s - box，定义为SF (x0, x1，…)。， xn−1)= y0|y1|…|yn−1其中yi:= F(xi, xi+1，…)ξ+ m−1)。作为主要结果，我们证明了•给定任何二次函数F: F2p→Fp，对应的S-Box SF / Fnp对于n≥3是不可逆的;•同样地，给定任何二次函数F: F3p→Fp，对应的S-Box SF / Fnp对于n≥5是不可逆的。此外，对于每个p≥3，我们通过函数F: Fmp→Fp和(2)(非平凡)二次函数F: F3p→Fp给出了前面定义的Fnp上的Lai-Massey构造的(1)推广，使得对于n∈{3,4}，SF over Fnp是可逆的。作为后续工作的一个开放问题，我们推测对于每一个m≥1，存在一个有限整数nmax(m)，使得SF / Fnp如之前通过二次函数F定义的，Fmp→Fp对于每一个n≥nmax(m)不可逆。最后，作为具体应用，我们提出了一种海绵哈希函数Poseidon的变体Neptune，它的非线性层是根据本文的结果设计的。我们表明，这种变体导致了关于波塞冬的具体乘法减少。
{"title":"Invertible Quadratic Non-Linear Layers for MPC-/FHE-/ZK-Friendly Schemes over Fnp Application to Poseidon","authors":"Lorenzo Grassi, Silvia Onofri, M. Pedicini, Luca Sozzi","doi":"10.46586/tosc.v2022.i3.20-72","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.20-72","url":null,"abstract":"Motivated by new applications such as secure Multi-Party Computation (MPC), Fully Homomorphic Encryption (FHE), and Zero-Knowledge proofs (ZK), many MPC-, FHE- and ZK-friendly symmetric-key primitives that minimize the number of multiplications over Fp for a large prime p have been recently proposed in the literature. This goal is often achieved by instantiating the non-linear layer via power maps x↦xd. In this paper, we start an analysis of new non-linear permutation functions over Fnp that can be used as building blocks in such symmetrickey primitives. Given a local map F : Fmp→ Fp, we limit ourselves to focus on S-Boxes over Fnp for n ≥ m defined as SF (x0, x1, . . . , xn−1) = y0|y1| . . . |yn−1 where yi := F(xi, xi+1, . . . , xi+m−1). As main results, we prove that• given any quadratic function F : F2p→ Fp, the corresponding S-Box SF over Fnp for n ≥ 3 is never invertible;• similarly, given any quadratic function F : F3p → Fp, the corresponding S-Box SF over Fnp for n ≥ 5 is never invertible.Moreover, for each p ≥ 3, we present (1st) generalizations of the Lai-Massey construction over Fnp defined as before via functions F : Fmp → Fp for each n = m ≥ 2 and (2nd) (non-trivial) quadratic functions F : F3p → Fp such that SF over Fnp for n ∈ {3, 4} is invertible. As an open problem for future work, we conjecture that for each m ≥ 1 there exists a finite integer nmax(m) such that SF over Fnp defined as before via a quadratic function F : Fmp →Fp is not invertible for each n ≥ nmax(m). Finally, as a concrete application, we propose Neptune, a variant of the sponge hash function Poseidon, whose non-linear layer is designed by taking into account the results presented in this paper. We show that this variant leads to a concrete multiplication reduction with respect to Poseidon.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"152 1","pages":"20-72"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79575634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.341-367
Ting Li, Yao Sun
Mixed Integer Linear Programming (MILP) solver has become one of the most powerful tools of searching for cryptographic characteristics. It has great significance to study the influencing factors of the efficiency of MILP models. For this goal, different types of MILP models should be constructed and carefully studied. As Boolean functions are the fundamental cryptographic components, in this paper, we study the descriptive models of Boolean functions. Here, a descriptive model of a Boolean function refers to a set of integer linear inequalities, where the set of the binary solutions to these inequalities is exactly the support of this Boolean function. Previously, it is hard to construct various types of descriptive models for study, one important reason is that only a few kinds of inequalities can be generated. On seeing this, a new approach, called SuperBall, is proposed to generate inequalities. The SuperBall approach is based on the method of undetermined coefficients, and it could generate almost all kinds of inequalities by appending appropriate constraints. Besides, the Sasaki-Todo Algorithm is also improved to construct the descriptive models from a set of candidate inequalities by considering both their sizes and strengths, while the strengths of descriptive models have not been considered in the previous works. As applications, we constructed several types of descriptive models for the Sboxes of Liliput, SKINNY-128, and AES. The experimental results first prove that the diversity of the inequalities generated by the SuperBall approach is good. More importantly, the results show that the strengths of descriptive model do affect the efficiencies, and although there is not a type of descriptive model having the best efficiency in all experiments, we did find a specific type of descriptive model which has the minimal size and relatively large strength, and the descriptive models of this type have better efficiencies in most of our experiments.
{"title":"SuperBall: A New Approach for MILP Modelings of Boolean Functions","authors":"Ting Li, Yao Sun","doi":"10.46586/tosc.v2022.i3.341-367","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.341-367","url":null,"abstract":"Mixed Integer Linear Programming (MILP) solver has become one of the most powerful tools of searching for cryptographic characteristics. It has great significance to study the influencing factors of the efficiency of MILP models. For this goal, different types of MILP models should be constructed and carefully studied. As Boolean functions are the fundamental cryptographic components, in this paper, we study the descriptive models of Boolean functions. Here, a descriptive model of a Boolean function refers to a set of integer linear inequalities, where the set of the binary solutions to these inequalities is exactly the support of this Boolean function. Previously, it is hard to construct various types of descriptive models for study, one important reason is that only a few kinds of inequalities can be generated. On seeing this, a new approach, called SuperBall, is proposed to generate inequalities. The SuperBall approach is based on the method of undetermined coefficients, and it could generate almost all kinds of inequalities by appending appropriate constraints. Besides, the Sasaki-Todo Algorithm is also improved to construct the descriptive models from a set of candidate inequalities by considering both their sizes and strengths, while the strengths of descriptive models have not been considered in the previous works. As applications, we constructed several types of descriptive models for the Sboxes of Liliput, SKINNY-128, and AES. The experimental results first prove that the diversity of the inequalities generated by the SuperBall approach is good. More importantly, the results show that the strengths of descriptive model do affect the efficiencies, and although there is not a type of descriptive model having the best efficiency in all experiments, we did find a specific type of descriptive model which has the minimal size and relatively large strength, and the descriptive models of this type have better efficiencies in most of our experiments.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"22 1","pages":"341-367"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86221532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.102-122
Fukang Liu, W. Meier, Santanu Sarkar, Takanori Isobe
The security of the post-quantum signature scheme Picnic is highly related to the difficulty of recovering the secret key of LowMC from a single plaintext-ciphertext pair. Since Picnic is one of the alternate third-round candidates in NIST post-quantum cryptography standardization process, it has become urgent and important to evaluate the security of LowMC in the Picnic setting. The best attacks on LowMC with full S-box layers used in Picnic3 were achieved with Dinur’s algorithm. For LowMC with partial nonlinear layers, e.g. 10 S-boxes per round adopted in Picnic2, the best attacks on LowMC were published by Banik et al. with the meet-in-the-middle (MITM) method.In this paper, we improve the attacks on LowMC in a model where memory consumption is costly. First, a new attack on 3-round LowMC with full S-box layers with negligible memory complexity is found, which can outperform Bouillaguet et al.’s fast exhaustive search attack and can achieve better time-memory tradeoffs than Dinur’s algorithm. Second, we extend the 3-round attack to 4 rounds to significantly reduce the memory complexity of Dinur’s algorithm at the sacrifice of a small factor of time complexity. For LowMC instances with 1 S-box per round, our attacks are shown to be much faster than the MITM attacks. For LowMC instances with 10 S-boxes per round, we can reduce the memory complexity from 32GB (238 bits) to only 256KB (221 bits) using our new algebraic attacks rather than the MITM attacks, while the time complexity of our attacks is about 23.2 ∼ 25 times higher than that of the MITM attacks. A notable feature of our new attacks (apart from the 4-round attack) is their simplicity. Specifically, only some basic linear algebra is required to understand them and they can be easily implemented.
{"title":"New Low-Memory Algebraic Attacks on LowMC in the Picnic Setting","authors":"Fukang Liu, W. Meier, Santanu Sarkar, Takanori Isobe","doi":"10.46586/tosc.v2022.i3.102-122","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.102-122","url":null,"abstract":"The security of the post-quantum signature scheme Picnic is highly related to the difficulty of recovering the secret key of LowMC from a single plaintext-ciphertext pair. Since Picnic is one of the alternate third-round candidates in NIST post-quantum cryptography standardization process, it has become urgent and important to evaluate the security of LowMC in the Picnic setting. The best attacks on LowMC with full S-box layers used in Picnic3 were achieved with Dinur’s algorithm. For LowMC with partial nonlinear layers, e.g. 10 S-boxes per round adopted in Picnic2, the best attacks on LowMC were published by Banik et al. with the meet-in-the-middle (MITM) method.In this paper, we improve the attacks on LowMC in a model where memory consumption is costly. First, a new attack on 3-round LowMC with full S-box layers with negligible memory complexity is found, which can outperform Bouillaguet et al.’s fast exhaustive search attack and can achieve better time-memory tradeoffs than Dinur’s algorithm. Second, we extend the 3-round attack to 4 rounds to significantly reduce the memory complexity of Dinur’s algorithm at the sacrifice of a small factor of time complexity. For LowMC instances with 1 S-box per round, our attacks are shown to be much faster than the MITM attacks. For LowMC instances with 10 S-boxes per round, we can reduce the memory complexity from 32GB (238 bits) to only 256KB (221 bits) using our new algebraic attacks rather than the MITM attacks, while the time complexity of our attacks is about 23.2 ∼ 25 times higher than that of the MITM attacks. A notable feature of our new attacks (apart from the 4-round attack) is their simplicity. Specifically, only some basic linear algebra is required to understand them and they can be easily implemented.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"19 1","pages":"102-122"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82853118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.73-101
Augustin Bariant, Clémence Bouvier, G. Leurent, Léo Perrin
Recent advanced Zero-Knowledge protocols, along with other high-level constructions such as Multi-Party Computations (MPC), have highlighted the need for a new type of symmetric primitives that are not optimized for speed on the usual platforms (desktop computers, servers, microcontrollers, RFID tags...), but for their ability to be implemented using arithmetic circuits.Several primitives have already been proposed to satisfy this need. In order to enable an efficient arithmetization, they operate over large finite fields, and use round functions that can be modelled using low degree equations. The impact of these properties on their security remains to be completely assessed. In particular, algebraic attacks relying on polynomial root-finding become extremely relevant. Such attacks work by writing the cryptanalysis as systems of polynomial equations over the large field, and solving them with off-the-shelf tools (SageMath, NTL, Magma, . . . ).The need for further analysis of these new designs has been recently highlighted by the Ethereum Foundation, as it issued bounties for successful attacks against round-reduced versions of several of them.In this paper, we show that the security analysis performed by the designers (or challenge authors) of four such primitives is too optimistic, and that it is possible to improve algebraic attacks using insights gathered from a careful study of the round function.First, we show that univariate polynomial root-finding can be of great relevance n practice, as it allows us to solve many of the Ethereum Foundation’s challenges on Feistel–MiMC. Second, we introduce a trick to essentially shave off two full rounds at little to no cost for Substitution-Permutation Networks (SPN). This can be combined with univariate (resp. multivariate) root-finding, which allowed to solve some challenges for Poseidon (resp. Rescue–Prime). Finally, we also find an alternative way to set up a system of equations to attack Ciminion, leading to much faster attacks than expected by the designers.
{"title":"Algebraic Attacks against Some Arithmetization-Oriented Primitives","authors":"Augustin Bariant, Clémence Bouvier, G. Leurent, Léo Perrin","doi":"10.46586/tosc.v2022.i3.73-101","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.73-101","url":null,"abstract":"Recent advanced Zero-Knowledge protocols, along with other high-level constructions such as Multi-Party Computations (MPC), have highlighted the need for a new type of symmetric primitives that are not optimized for speed on the usual platforms (desktop computers, servers, microcontrollers, RFID tags...), but for their ability to be implemented using arithmetic circuits.Several primitives have already been proposed to satisfy this need. In order to enable an efficient arithmetization, they operate over large finite fields, and use round functions that can be modelled using low degree equations. The impact of these properties on their security remains to be completely assessed. In particular, algebraic attacks relying on polynomial root-finding become extremely relevant. Such attacks work by writing the cryptanalysis as systems of polynomial equations over the large field, and solving them with off-the-shelf tools (SageMath, NTL, Magma, . . . ).The need for further analysis of these new designs has been recently highlighted by the Ethereum Foundation, as it issued bounties for successful attacks against round-reduced versions of several of them.In this paper, we show that the security analysis performed by the designers (or challenge authors) of four such primitives is too optimistic, and that it is possible to improve algebraic attacks using insights gathered from a careful study of the round function.First, we show that univariate polynomial root-finding can be of great relevance n practice, as it allows us to solve many of the Ethereum Foundation’s challenges on Feistel–MiMC. Second, we introduce a trick to essentially shave off two full rounds at little to no cost for Substitution-Permutation Networks (SPN). This can be combined with univariate (resp. multivariate) root-finding, which allowed to solve some challenges for Poseidon (resp. Rescue–Prime). Finally, we also find an alternative way to set up a system of equations to attack Ciminion, leading to much faster attacks than expected by the designers.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"183 1","pages":"73-101"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76133187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-09DOI: 10.46586/tosc.v2022.i3.123-151
Akinori Hosoyamada, Akiko Inoue, Ryoma Ito, Tetsu Iwata, Kazuhiko Minematsu, Ferdinand Sibleyras, Yosuke Todo
Rocca is an authenticated encryption with associated data scheme for beyond 5G/6G systems. It was proposed at FSE 2022/ToSC 2021(2), and the designers make a security claim of achieving 256-bit security against key-recovery and distinguishing attacks, and 128-bit security against forgery attacks (the security claim regarding distinguishing attacks was subsequently weakened in the full version in ePrint 2022/116). A notable aspect of the claim is the gap between the privacy and authenticity security. In particular, the security claim regarding key-recovery attacks allows an attacker to obtain multiple forgeries through the decryption oracle. In this paper, we first present a full key-recovery attack on Rocca. The data complexity of our attack is 2128 and the time complexity is about 2128, where the attack makes use of the encryption and decryption oracles, and the success probability is almost 1. The attack recovers the entire 256-bit key in a single-key and nonce-respecting setting, breaking the 256-bit security claim against key-recovery attacks. We then extend the attack to various security models and discuss several countermeasures to see the feasibility of the security claim. Finally, we consider a theoretical question of whether achieving the security claim of Rocca is possible in the provable security paradigm. We present both negative and positive results to the question.
{"title":"Cryptanalysis of Rocca and Feasibility of Its Security Claim","authors":"Akinori Hosoyamada, Akiko Inoue, Ryoma Ito, Tetsu Iwata, Kazuhiko Minematsu, Ferdinand Sibleyras, Yosuke Todo","doi":"10.46586/tosc.v2022.i3.123-151","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i3.123-151","url":null,"abstract":"Rocca is an authenticated encryption with associated data scheme for beyond 5G/6G systems. It was proposed at FSE 2022/ToSC 2021(2), and the designers make a security claim of achieving 256-bit security against key-recovery and distinguishing attacks, and 128-bit security against forgery attacks (the security claim regarding distinguishing attacks was subsequently weakened in the full version in ePrint 2022/116). A notable aspect of the claim is the gap between the privacy and authenticity security. In particular, the security claim regarding key-recovery attacks allows an attacker to obtain multiple forgeries through the decryption oracle. In this paper, we first present a full key-recovery attack on Rocca. The data complexity of our attack is 2128 and the time complexity is about 2128, where the attack makes use of the encryption and decryption oracles, and the success probability is almost 1. The attack recovers the entire 256-bit key in a single-key and nonce-respecting setting, breaking the 256-bit security claim against key-recovery attacks. We then extend the attack to various security models and discuss several countermeasures to see the feasibility of the security claim. Finally, we consider a theoretical question of whether achieving the security claim of Rocca is possible in the provable security paradigm. We present both negative and positive results to the question.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"30 1","pages":"123-151"},"PeriodicalIF":3.5,"publicationDate":"2022-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83725024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lightweight cryptography ensures cryptography applications to devices with limited resources. Low-area implementations of linear layers usually play an essential role in lightweight cryptography. The previous works have provided plenty of methods to generate low-area implementations using 2-input xor gates for various linear layers. However, it is still challenging to search for smaller implementations using two or more inputs xor gates. This paper, inspired by Banik et al., proposes a novel approach to construct a quantity of lower area implementations with (n + 1)- input gates based on the given implementations with n-input gates. Based on the novel algorithm, we present the corresponding search algorithms for n = 2 and n = 3, which means that we can efficiently convert an implementation with 2-input xor gates and 3-input xor gates to lower-area implementations with 3-input xor gates and 4-input xor gates, respectively.We improve the previous implementations of linear layers for many block ciphers according to the area with these search algorithms. For example, we achieve a better implementation with 4-input xor gates for AES MixColumns, which only requires 243 GE in the STM 130 nm library, while the previous public result is 258.9 GE. Besides, we obtain better implementations for all 5500 lightweight matrices proposed by Li et al. at FSE 2019, and the area for them is decreased by about 21% on average.
{"title":"More Inputs Makes Difference: Implementations of Linear Layers Using Gates with More Than Two Inputs","authors":"Qun Liu, Weijia Wang, Ling Sun, Yanhong Fan, Lixuan Wu, Meiqin Wang","doi":"10.46586/tosc.v2022.i2.351-378","DOIUrl":"https://doi.org/10.46586/tosc.v2022.i2.351-378","url":null,"abstract":"Lightweight cryptography ensures cryptography applications to devices with limited resources. Low-area implementations of linear layers usually play an essential role in lightweight cryptography. The previous works have provided plenty of methods to generate low-area implementations using 2-input xor gates for various linear layers. However, it is still challenging to search for smaller implementations using two or more inputs xor gates. This paper, inspired by Banik et al., proposes a novel approach to construct a quantity of lower area implementations with (n + 1)- input gates based on the given implementations with n-input gates. Based on the novel algorithm, we present the corresponding search algorithms for n = 2 and n = 3, which means that we can efficiently convert an implementation with 2-input xor gates and 3-input xor gates to lower-area implementations with 3-input xor gates and 4-input xor gates, respectively.We improve the previous implementations of linear layers for many block ciphers according to the area with these search algorithms. For example, we achieve a better implementation with 4-input xor gates for AES MixColumns, which only requires 243 GE in the STM 130 nm library, while the previous public result is 258.9 GE. Besides, we obtain better implementations for all 5500 lightweight matrices proposed by Li et al. at FSE 2019, and the area for them is decreased by about 21% on average.","PeriodicalId":37077,"journal":{"name":"IACR Transactions on Symmetric Cryptology","volume":"63 1","pages":"351-378"},"PeriodicalIF":3.5,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91033573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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