Encryption and decryption devices for public-key cryptosystems and recording medium with their processing programs recorded thereon

The present invention relates to encryption and decryption devices for use in public-key cryptosystems and a recording medium with their processing programs recorded thereon. In a public-key cryptosystem based on a multiplicative group, n=pq, where p and q are odd primes, and g, selected from (Z/nZ)* such that g=gmod phas an order of p in (Z/ pZ)*, are made public. A plaintext m, a random number and n are used to calculate m+rn, and n and g are used to compute C=gmod n to generate it as ciphertext. For the ciphertext C, C mod pis calculated, then C=Cmod pis calculated to obtain (C)/p=L(C), and L(C) is multiplied by a secret key L(g)mod p to obtain the plaintext m.