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Digital Signature Schemes over the Ring Z[e2πi/5]

Published: 22 October 2019 Publication History

Abstract

This paper proposes an extended RSA digital signature scheme and extended ElGamal digital signature schemes with appendix and with message recovery over the algebraic integer ring Z[e2πi/5] of the cyclotomic field Q[e2πi/5]. In these digital signature schemes, the extended Euler-phi function is φ(n) = (p4 - 1) (q4 - 1) compared to the classical Euler-phi function φ(n)=(p-1)(q-1) where n is a product of two large primes p and q. The encryption exponent is chosen to be coprime to the extended Euler-phi function. Thus, the encryption exponents have more options, which provides more security than that of the classical case. The securities of digital signature schemes depend on the difficulty of factoring large integers into a product of primes, and logarithmic computations in the ring Z[e2πi/5] Some numerical examples are given.

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T. ElGamal. 1985. A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory, 31,469--472.
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CSAE '19: Proceedings of the 3rd International Conference on Computer Science and Application Engineering
October 2019
942 pages
ISBN:9781450362948
DOI:10.1145/3331453
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 October 2019

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Author Tags

  1. Algebraic integer ring
  2. Cryptography
  3. Digital signature
  4. Discrete logarithm

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CSAE 2019

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Overall Acceptance Rate 368 of 770 submissions, 48%

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