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Title:
A study on the fast ElGamal encryption
Authors: Kim Gyu-Chol, 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.
ePrint: https://eprint.iacr.org/2018/930
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