Polynomial interpolation of cryptographic functions related to Diffie-Hellman and discrete logarithm problem

Authors:
Eike Kiltz;Arne Winterhof
Affiliations:
Lehrstuhl Mathematik & Informatik, Fakultäät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany;Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, c/o Johannes Kepler University Linz, Altenbergerstraíe 69, 4040 Linz, Austria
Venue:
Discrete Applied Mathematics - Special issue: Coding and cryptography
Year:
2006

Citing 10
Cited 4

Algorithmic number theory

Algorithmic number theory
Modern computer algebra

Modern computer algebra
Polynomial Interpolation of the Discrete Logarithm

Designs, Codes and Cryptography
Handbook of Applied Cryptography

Handbook of Applied Cryptography
On the linear complexity profile of explicit nonlinear pseudorandom numbers

Information Processing Letters
Polynomial Interpolation of the Elliptic Curve and XTR Discrete Logarithm

COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
A Tool Box of Cryptographic Functions Related to the Diffie-Hellman Function

INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
Interpolation of the elliptic curve Diffie-Hellman mapping

AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
A polynomial form for logarithms modulo a prime (Corresp.)

IEEE Transactions on Information Theory
Incomplete Character Sums and Polynomial Interpolation of the Discrete Logarithm

Finite Fields and Their Applications

Interpolation of the Double Discrete Logarithm

WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Interpolation of functions related to the integer factoring problem

WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography
Polynomial approximation of bilinear Diffie--Hellman maps

Finite Fields and Their Applications
Polynomial representations of the Lucas logarithm

Finite Fields and Their Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Recently, the first author introduced some cryptographic functions closely related to the Diffie-Hellman problem called P-Diffie-Hellman functions. We show that the existence of a low-degree polynomial representing a P-Diffie-Hellman function on a large set would lead to an efficient algorithm for solving the Diffie-Hellman problem. Motivated by this result we prove lower bounds on the degree of such interpolation polynomials. Analogously, we introduce a class of functions related to the discrete logarithm and show similar reduction and interpolation results.