论文信息 - A One Way Function Based on Ideal Arithmetic in Number Fields

A One Way Function Based on Ideal Arithmetic in Number Fields

We present a new one way function based on the difficulty of finding shortest vectors in lattices. This new function consists of exponentiation of an ideal in an order of a number field and multiplication by an algebraic number which can both be performed in polynomial time. The best known algorithm for inverting this function is exponential in the degree of the lattices involved.

Sachar Paulus | Johannes A. Buchmann

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

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

[3] Ravi Kannan,et al. Minkowski's Convex Body Theorem and Integer Programming , 1987, Math. Oper. Res..

[4] C. P. Schnorr,et al. A Hierarchy of Polynomial Time Lattice Basis Reduction Algorithms , 1987, Theor. Comput. Sci..

[5] Christoph Thiel,et al. Short Proofs Using Compact Representations of Algebraic Integers , 1995, J. Complex..

[6] Johannes Buchmann,et al. Quadratic fields and cryptography , 1991 .

[7] Johannes A. Buchmann,et al. On the Computation of Discrete Logarithms in Class Groups , 1990, CRYPTO.

[8] N. Koblitz. Elliptic curve cryptosystems , 1987 .

[9] Bernd Meyer,et al. Tools for Proving Zero Knowledge , 1992, EUROCRYPT.

[10] O. Taussky. Some computational problems in algebraic number theory , 1954 .

[11] Andrew M. Odlyzko,et al. Discrete Logarithms in Finite Fields and Their Cryptographic Significance , 1985, EUROCRYPT.

[12] Johannes Buchmann,et al. LiDIA : a library for computational number theory , 1995 .

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

[14] Jeffrey Shallit,et al. Algorithmic Number Theory , 1996, Lecture Notes in Computer Science.