Optimising Gröbner Bases on Bivium

Eibach, Tobias; Völkel, Gunnar; Pilz, Enrico

doi:10.1007/s11786-009-0016-7

Cited by 11 publications

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Biviumb: a polynomial system originated from the problem of recovering the internal states of the stream cipher Bivium-B (Raddum, 2006;Eibach and Völkel, 2010), which is a reduced version of stream cipher Trivium. By setting the 177-bit internal states as variables, and using 160-bit keystream, we can generate a polynomial system with 177 variables, 160 polynomials and degree 3.…”

Section: Theorem 19 Letmentioning

confidence: 99%

On the efficiency of solving Boolean polynomial systems with the characteristic set method

Huang

Sun

Lin

2021

Journal of Symbolic Computation

View full text Add to dashboard Cite

An improved characteristic set algorithm for solving Boolean polynomial systems is proposed. This algorithm is based on the idea of converting all the polynomials into monic ones by zero decomposition, and using additions to obtain pseudo-remainders. Three important techniques are applied in the algorithm. The first one is eliminating variables by new generated linear polynomials. The second one is optimizing the strategy of choosing polynomial for zero decomposition. The third one is to compute add-remainders to eliminate the leading variable of new generated monic polynomials. By analyzing the depth of the zero decomposition tree, we present some complexity bounds of this algorithm, which are lower than the complexity bounds of previous characteristic set algorithms. Extensive experimental results show that this new algorithm is more efficient than previous characteristic set algorithms for solving Boolean polynomial systems.

show abstract

Section: Theorem 19 Letmentioning

confidence: 99%

On the efficiency of solving Boolean polynomial systems with the characteristic set method

Huang

Sun

Lin

2021

Journal of Symbolic Computation

View full text Add to dashboard Cite

show abstract

“…Non-deterministic Oracle Backdoor Sets correspond to cryptographic attacks, where NP-oracles are used to solve subproblems constructed for a specific Backdoor set. For instance, very similar approach was applied to cryptanalysis of the widely known Bivium and Trivium ciphers (Eibach, Pilz, and Völkel 2008;Semenov and Zaikin 2016;Eibach, Völkel, and Pilz 2010;Huang and Lin 2011).…”

Section: Guess-and-determine Attacks On Cryptographic Functionsmentioning

confidence: 99%

On Cryptographic Attacks Using Backdoors for SAT

Семенов

Zaikin

Otpuschennikov

et al. 2018

AAAI

View full text Add to dashboard Cite

Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled efficiently by identifying and exploiting a subset of formula's variables called backdoor set (or simply backdoors). This paper proposes a new class of backdoor sets for SAT used in the context of cryptographic attacks, namely guess-and-determine attacks. The idea is to identify the best set of backdoor variables subject to a statistically estimated hardness of the guess-and-determine attack using a SAT solver. Experimental results on weakened variants of the renowned encryption algorithms exhibit advantage of the proposed approach compared to the state of the art in terms of the estimated hardness of the resulting guess-and-determine attacks.

show abstract

“…In fact, by using the inverse of the difference system governing the state, some opponent may recover the initial state containing the key by attacking any internal state. This technique has been used, for instance, to attack Trivium cipher and its simplified version Bivium (see [12,14] and Section 5 and 6).…”

Section: Introductionmentioning

confidence: 99%

Stream/block ciphers, difference equations and algebraic attacks

Scala¹,

Tiwari²

2020

Preprint

View full text Add to dashboard Cite

In this paper we introduce a general class of stream and block ciphers that are defined by means of systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers". Many important ciphers such as systems of LFSRs, Trivium/Bivium and KeeLoq are difference ciphers. To the purpose of studying their underlying explicit difference systems, we introduce key notions as state transition endomorphisms and show conditions for their invertibility. Reducible and periodic systems are also considered. We then propose general algebraic attacks to difference ciphers which are experimented by means of Bivium and KeeLoq.

show abstract

Optimising Gröbner Bases on Bivium

Cited by 11 publications

References 17 publications

On the efficiency of solving Boolean polynomial systems with the characteristic set method

On the efficiency of solving Boolean polynomial systems with the characteristic set method

On Cryptographic Attacks Using Backdoors for SAT

Stream/block ciphers, difference equations and algebraic attacks

Contact Info

Product

Resources

About