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=g m+rn mod n to generate it as ciphertext. For the ciphertext C, C mod p2 is calculated, then C p=C p-1 mod p2 is calculated to obtain (C p-1)/p=L(C p), and L(C p) is multiplied by a secret key L(g p)-1 mod p to obtain the plaintext m.