A Public Key Cryptosystem Using a Group of Permutation Polynomials
| Autor: | Anupam Saikia, Rajesh P. Singh, Bhaba Kumar Sarma |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Discrete mathematics
021110 strategic defence & security studies Group (mathematics) business.industry General Mathematics 010102 general mathematics 0211 other engineering and technologies Public key cryptosystem 02 engineering and technology Encryption 01 natural sciences Permutation Finite field Cryptosystem Trapdoor function 0101 mathematics Abelian group business Mathematics |
| Zdroj: | Tatra Mountains Mathematical Publications. 77:139-162 |
| ISSN: | 1210-3195 |
| DOI: | 10.2478/tmmp-2020-0013 |
| Popis: | In this paper we propose an efficient multivariate encryption scheme based on permutation polynomials over finite fields. We single out a commutative group ℒ(q, m) of permutation polynomials over the finite field F q m. We construct a trapdoor function for the cryptosystem using polynomials in ℒ(2, m), where m =2 k for some k ≥ 0. The complexity of encryption in our public key cryptosystem is O(m 3) multiplications which is equivalent to other multivariate public key cryptosystems. For decryption only left cyclic shifts, permutation of bits and xor operations are used. It uses at most 5m 2+3m – 4 left cyclic shifts, 5m 2 +3m + 4 xor operations and 7 permutations on bits for decryption. |
| Databáze: | OpenAIRE |
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