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Analysis of the stream cipher QUAD
Čurilla, Marcel ; Holub, Štěpán (advisor) ; Příhoda, Pavel (referee)
Title: Analysis of the stream cipher QUAD Author: Marcel Čurilla Department: Katedra algebry Supervisor: doc. Mgr. Štěpán Holub, Ph.D. Abstract: Stream cipher QUAD was introduced in 2006 on Eurocrypt by Côme Ber- bain, Henri Gilbert a Jacques Patarin cite quad. The authors showed a reduction of this cipher for the problem of solving m quadratic equations of n variables over finite fields known as the MQ problem. For simplicity, they considered only the case of the field GF(2). In this thesis I introduce this stream cipher. I show the proof (reduction) of safety ciphers QUAD for MQ problem over any finite field GF(q). I describe the basic met- hods for the solution of system of quadratic equations over finite fields, linearization and relinearization. I focus on XL algorithm - which is currently the fastest algo- rithm for solving quadratic systems. This algorithm was designed precisely to deal with overdefined quadratic systems. While analyzing the cipher QUAD I show for what instance is a cipher QUAD breakable and vice versa for what instance is the security guaranteed. Keywords: stream cipher, QUAD, MQ problem, algorithm XL, 1
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Analysis of the stream cipher QUAD
Čurilla, Marcel ; Holub, Štěpán (advisor) ; Příhoda, Pavel (referee)
Title: Analysis of the stream cipher QUAD Author: Marcel Čurilla Department: Katedra algebry Supervisor: doc. Mgr. Štěpán Holub, Ph.D. Abstract: Stream cipher QUAD was introduced in 2006 on Eurocrypt by Côme Ber- bain, Henri Gilbert a Jacques Patarin cite quad. The authors showed a reduction of this cipher for the problem of solving m quadratic equations of n variables over finite fields known as the MQ problem. For simplicity, they considered only the case of the field GF(2). In this thesis I introduce this stream cipher. I show the proof (reduction) of safety ciphers QUAD for MQ problem over any finite field GF(q). I describe the basic met- hods for the solution of system of quadratic equations over finite fields, linearization and relinearization. I focus on XL algorithm - which is currently the fastest algo- rithm for solving quadratic systems. This algorithm was designed precisely to deal with overdefined quadratic systems. While analyzing the cipher QUAD I show for what instance is a cipher QUAD breakable and vice versa for what instance is the security guaranteed. Keywords: stream cipher, QUAD, MQ problem, algorithm XL, 1
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