In a public-key cryptosystem based on a multiplicative group, n=p.sup.2 q, where p and q are odd primes, and g, selected from (Z/nZ)* such that g.sub.p =g.sup.r-1 mod p.sup.2 has an order of p in (Z/ p.sup.2 Z)*, 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.sup.m+rn mod n to generate it as ciphertext. For the ciphertext C, C mod p.sup.2 is calculated, then C.sub.p =C.sup.p-1 mod p.sup.2 is calculated to obtain (C.sub.p-1)/p=L(C.sub.p), and L(C.sub.p) is multiplied by a secret key L(g.sub.p).sup.-1 mod p to obtain the plaintext m.

En un cryptosystem de la pu'blico-llave basado en un grupo multiplicative, n=p.sup.2 q, donde están impares p y q prepara, y g, seleccionado de (Z/nZ) * tales que g.sub.p = g.sup.r-1 la MOD p.sup.2 tiene una orden de p adentro (z p.sup.2 Z) *, se hacen público. Un plaintext m, un número al azar y n se utilizan para calcular m+rn, y n y g se utilizan para computar MOD n de C=g.sup.m+rn para generarla como texto cifrado. Para el texto cifrado C, se calcula la MOD p.sup.2 de C, después C.sub.p = C.sup.p-1 la MOD p.sup.2 se calcula para obtener (C.sub.p-1)/p=L(C.sub.p), y L(C.sub.p) es multiplicado por una MOD secreta p de la llave L(g.sub.p).sup.-1 para obtener el plaintext m.

 
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