Algorithmic number theory
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
Incomplete Character Sums and Polynomial Interpolation of the Discrete Logarithm
Finite Fields and Their Applications
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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.