Trapdoor one-way permutations and multivariate polynomials
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This article is divided into three parts. The first part describes the known candidates of trapdoor one-way permutations. The second part presents a new algorithm, called D*. As we will see, this algorithm is not secure. However, in the third part, D* will be a useful tool to present our new candidate trapdoor one-way permutation, called D**. This candidate is based on properties of multivariate polynomials on finite fields, and has similar characteristics to T. Matsumoto and H. Imai's schemes.
What makes trapdoor one-way permutations particularly interesting is the fact that they immediately provide ciphering, signature, and authentication asymmetric schemes.
Our candidate performs excellently in secret key, and secret key computations can be implemented in low-cost smart-cards, i.e. without co-processors. An extended version of this paper can be obtained from the authors.
KeywordsElliptic Curve Finite Field Elliptic Curf Total Degree Quadratic Residue
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