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

In a public-key cryptosystem based on a multiplicative group, n=p2q, where p and q are odd primes, and g, selected from (Z/nZ)* such that gp=gr-1 mod p2 has an order of p in (Z/ p2Z)*, 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=gm+rn mod n to generate it as ciphertext. For the ciphertext C, C mod p2 is calculated, then Cp=Cp-1 mod p2 is calculated to obtain (Cp-1)/p=L(Cp), and L(Cp) is multiplied by a secret key L(gp)-1 mod p to obtain the plaintext m.