论文信息 - Approximate Power Roots in Zm - 字舞流文

Approximate Power Roots in Zm

Some algorithms to search for power residues close to a desired value are reported. They are used in the cryptanalysis of low exponent RSA with partially known clear text.

Germán Sáez | Ismael Jiménez Calvo | I. J. Calvo | Germán Sáez

[1] Don Coppersmith,et al. Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities , 1997, Journal of Cryptology.

[2] Carl Pomerance,et al. The Quadratic Sieve Factoring Algorithm , 1985, EUROCRYPT.

[3] E. Brickell,et al. Cryptanalysis: a survey of recent results , 1988, Proc. IEEE.

[4] Johan Håstad,et al. Solving Simultaneous Modular Equations of Low Degree , 1988, SIAM J. Comput..

[5] Henri Cohen,et al. A course in computational algebraic number theory , 1993, Graduate texts in mathematics.

[6] A. K. Lenstra,et al. Factoring polynomials with integer coefficients , 1982 .

[7] B. Vallée. Generation of elements with small modular squares and provably fast integer factoring algorithms , 1991 .

[8] Adi Shamir,et al. A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[9] László Lovász,et al. Factoring polynomials with rational coefficients , 1982 .

[10] Robert D. Silverman. The multiple polynomial quadratic sieve , 1987 .

[11] René Peralta,et al. A Quadratic Sieve on the n-Dimensional Cube , 1992, CRYPTO.

[12] I. Niven,et al. An introduction to the theory of numbers , 1961 .