Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
Integer and combinatorial optimization
Integer and combinatorial optimization
Attacking Bivium using SAT solvers
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Trivium: a stream cipher construction inspired by block cipher design principles
ISC'06 Proceedings of the 9th international conference on Information Security
Hill climbing algorithms and Trivium
SAC'10 Proceedings of the 17th international conference on Selected areas in cryptography
Cold boot key recovery by solving polynomial systems with noise
ACNS'11 Proceedings of the 9th international conference on Applied cryptography and network security
Cryptanalysis of the light-weight cipher a2u2
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Differential and linear cryptanalysis using mixed-integer linear programming
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
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Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations over GF (2) into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over *** and formulate the problem of finding a 0-1-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several algorithms in the field of combinatorial optimization in order to find a solution for the problem and recover the initial state of Bivium. In particular this gives us an attack on Bivium B in estimated time complexity of 263.7 seconds. But this kind of attack is also applicable to other cryptographic algorithms.