Analysis of a public key approach based on polynomial substitution
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
How to prove yourself: practical solutions to identification and signature problems
Proceedings on Advances in cryptology---CRYPTO '86
On the generation of multivariate polynomials which are hard to factor
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Attacks on the birational permutation signature schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
On the security of stepwise triangular systems
Designs, Codes and Cryptography
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
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Many public key cryptographic schemes (such as cubic RSA) are based on low degree polynomials whose inverses are high degree polynomials. These functions are very easy to compute but time consuming to invert even by their legitimate users. To overcome this problem, it is natural to consider the class of birational permutations f over k-tuples of numbers, in which both f and f-1 are low degree rational functions. In this paper we develop two new families of birational permutations, and discuss their cryptographic applications.