Abstract

In the last few years, there have been several attempts to build identification protocols that do not rely on arithmetical operations with large numbers but only use simple operations (see [10, 8]). One was presented at the CRYPTO 89 rump session ([8]) and depends on the so-called Permuted Kernel problem (PKP). Another appeared in the CRYPTO 93 proceedings and is based on the syndrome decoding problem (SD) form the theory of error correcting codes ([11]). In this paper, we introduce a new scheme of the same family with the distinctive character that both the secret key and the public identification key can be taken to be of short length. By short, we basically mean the usual size of conventional symmetric cryptosystems. As is known, the possibility of using short keys has been a challenge in public key cryptography and has practical applications. Our scheme relies on a combinatorial problem which we call Constrained Linear Equations (CLE in short) and which consists of solving a set of linear equations modulo some small prime q, the unknowns being subject to belong to a specific subset of the integers mod q. Thus, we enlarge the set of tools that can be used in cryptography.

Citations

1130	Random oracles are practical: A paradigm for designing efficient protocols - Bellare, Rogaway - 1993
893	The knowledge complexity of interactive proof systems - Goldwasser, Micali, et al. - 1989
707	How to prove yourself: Practical solutions to identification and signature problems - Fiat, Shamir - 1986
325	The MD4 message digest algorithm - RIVEST - 1991
289	Zero Knowledge Proofs of Identity - Feige, Fiat, et al. - 1987
50	A new identification scheme based on syndrome decoding - Stern - 1993
36	An Efficient Identification Scheme Based on Permuted Kernels - Shamir - 1990
24	On the security of some cryptosystems based on error-correcting codes - Chabaud - 1995
7	On the Security of the Permuted Kernel Identification Scheme - Baritaud, Campana, et al. - 1992
4	An alternative to the Fiat-Shamir protocol - Stern - 1990
3	Improved algorithms for the permuted kernel prolem - Patarin, Chauvaud - 1994