### A study on the fast ElGamal encryption

Kim Gyu-Chol and Li Su-Chol

##### Abstract

ElGamal cryptosystem is typically developed in the multiplicative group $\mathbb{Z}_p^*$ ($p$ 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 $\mathbb Z_p^*$, various variants such as ECElGamal (ElGamal in elliptic curve group), CRTElGamal (ElGamal in subgroup of $\mathbb Z_n^*$ where $n=pq$ and $p,q,(p-1)/2,(q-1)/2$ are primes) have already been used for the semantic security. In this paper, for the fast decryption, we reduced the private CRT exponent $x_p$ ($= x mod (p - 1)$) and $x_q$ ($= x mod (q-1)$)maintaining full sized private exponent $x$ ($0<x<n$) in CRTElGamal as reducing $d_p$ ($= d mod (p - 1)$) and $d_q$ ($= d mod (q-1)$) 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.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
RSAElGamalpublic keyRebalanced RSACRT
Contact author(s)
kgc841110 @ star-co net kp
History
Short URL
https://ia.cr/2018/930

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},
note = {\url{https://eprint.iacr.org/2018/930}},
url = {https://eprint.iacr.org/2018/930}
}

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