Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic ...Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.展开更多
A linearization attack on the Key Stream Generator （KSG） of the modified Eo algorithm proposed by Hermelin [Proceedings of ICISC＇99, Springer LNCS 1787, 2000, 17-29] is given in this paper. The initial value can be...A linearization attack on the Key Stream Generator （KSG） of the modified Eo algorithm proposed by Hermelin [Proceedings of ICISC＇99, Springer LNCS 1787, 2000, 17-29] is given in this paper. The initial value can be recovered by a linearization attack with O（2^60.52） operations by solving a System of Linear Equations （SLE） with at most 2^20.538 unknowns. Frederik Armknecht [Cryptology ePrint Archive, 2002/191] proposed a linearization attack on the KSG olEo algorithm with O（2^70.341） operations by solving an SLE with at most 2^24.056 unknowns, so the modification proposed by Hermelin reduces the ability or E0 to resist the linearization attack by comparing with the results ofFrederik Armknecht.展开更多
文摘Quadratic-field cryptosystem is a cryptosystem built from discrete logarithm problem in ideal class groups of quadratic fields(CL-DLP). The problem on digital signature scheme based on ideal class groups of quadratic fields remained open, because of the difficulty of computing class numbers of quadratic fields. In this paper, according to our researches on quadratic fields, we construct the first digital signature scheme in ideal class groups of quadratic fields, using q as modulus, which denotes the prime divisors of ideal class numbers of quadratic fields. Security of the new signature scheme is based fully on CL-DLP. This paper also investigates realization of the scheme, and proposes the concrete technique. In addition, the technique introduced in the paper can be utilized to realize signature schemes of other kinds.
文摘A linearization attack on the Key Stream Generator （KSG） of the modified Eo algorithm proposed by Hermelin [Proceedings of ICISC＇99, Springer LNCS 1787, 2000, 17-29] is given in this paper. The initial value can be recovered by a linearization attack with O（2^60.52） operations by solving a System of Linear Equations （SLE） with at most 2^20.538 unknowns. Frederik Armknecht [Cryptology ePrint Archive, 2002/191] proposed a linearization attack on the KSG olEo algorithm with O（2^70.341） operations by solving an SLE with at most 2^24.056 unknowns, so the modification proposed by Hermelin reduces the ability or E0 to resist the linearization attack by comparing with the results ofFrederik Armknecht.
