Paper 2018/930

A study on the fast ElGamal encryption

Kim Gyu-Chol and Li Su-Chol

Abstract

ElGamal cryptosystem is typically developed in the multiplicative group Zp (p is a prime number), but it can be applied to the other groups in which discrete logarithm problem should be computationally infeasible. Practically, instead of ElGamal in Zp, various variants such as ECElGamal (ElGamal in elliptic curve group), CRTElGamal (ElGamal in subgroup of Zn where n=pq and p,q,(p1)/2,(q1)/2 are primes) have already been used for the semantic security. In this paper, for the fast decryption, we reduced the private CRT exponent xp (=xmod(p1)) and xq (=xmod(q1))maintaining full sized private exponent x (0<x<n) in CRTElGamal as reducing dp (=dmod(p1)) and dq (=dmod(q1)) in RSA for the fast decryption. (i.e. as in rebalanced RSA). In this case, unlike rebalanced RSA, decryption of CRTElGamal can be done faster without losing of encryption speed. As a result, it is possible to propose the fast public key cryptosystem that has fast encryption and fast decryption.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
RSAElGamalpublic keyRebalanced RSACRT
Contact author(s)
kgc841110 @ star-co net kp
History
2018-10-02: received
Short URL
https://ia.cr/2018/930
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2018/930,
      author = {Kim Gyu-Chol and Li Su-Chol},
      title = {A study on the fast {ElGamal} encryption},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/930},
      year = {2018},
      url = {https://eprint.iacr.org/2018/930}
}
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