Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the pe...Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the perspective of Fibonacci NFSRs.It is shown that an n-stage Trivium-like NFSR cannot be equivalent to an n-stage Fibonacci NFSR,which is proved by showing the existence of“collision initial states”.As an intermediate conclusion,a necessary and sufficient condition for a kind of linear degeneracy of a Trivium-like NFSR is obtained from the persepective of interleaved sequences.Moreover,the smallest stage number of a Fibonacci NFSR that can generate all the output sequences of an n-stage Trivium-like NFSR is shown to be greater than n-7 and this value is no less than 371=287+min{93,84,111}specifically for the 288-stage Galois NFSR used in Trivium.These results contradict the existence of a equivalent Fibonacci model of Trivium NFSR of small stage,which implies that Trivium algorithm possesses a fair degree of immunity against“structure attack”.展开更多
The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In ...The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In particular,the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao,et al.at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu,et al.at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks.Consequently,at this state of the art,whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly,that is,the number of terms.Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now.Some effective cube construction methods were proposed for experimental cube attacks,but not applicable to division property based cube attacks.In this paper,the authors propose a heuristic cube criterion and a cube sieve algorithm,which can be combined with the three-subset division property to recover a number of superpolies.Applied to815-round Trivium,the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48.The success rate is 94.56%.There are 165 non-constant superpolies with degree less than 14.In order to demonstrate the significance of the new algorithm,the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium.The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12371526,61872383,61802430,and 62202494。
文摘Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the perspective of Fibonacci NFSRs.It is shown that an n-stage Trivium-like NFSR cannot be equivalent to an n-stage Fibonacci NFSR,which is proved by showing the existence of“collision initial states”.As an intermediate conclusion,a necessary and sufficient condition for a kind of linear degeneracy of a Trivium-like NFSR is obtained from the persepective of interleaved sequences.Moreover,the smallest stage number of a Fibonacci NFSR that can generate all the output sequences of an n-stage Trivium-like NFSR is shown to be greater than n-7 and this value is no less than 371=287+min{93,84,111}specifically for the 288-stage Galois NFSR used in Trivium.These results contradict the existence of a equivalent Fibonacci model of Trivium NFSR of small stage,which implies that Trivium algorithm possesses a fair degree of immunity against“structure attack”.
基金supported by the National Natural Science Foundation of China under Grant No.61672533。
文摘The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In particular,the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao,et al.at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu,et al.at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks.Consequently,at this state of the art,whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly,that is,the number of terms.Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now.Some effective cube construction methods were proposed for experimental cube attacks,but not applicable to division property based cube attacks.In this paper,the authors propose a heuristic cube criterion and a cube sieve algorithm,which can be combined with the three-subset division property to recover a number of superpolies.Applied to815-round Trivium,the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48.The success rate is 94.56%.There are 165 non-constant superpolies with degree less than 14.In order to demonstrate the significance of the new algorithm,the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium.The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.
