초록

A cryptography system improves the decryption speed in the RSA algorithm by taking advantage of certain subgroups of Z.sub.n *. The cryptography system employs a new family of trapdoor permutations based on exponentiation in subgroups of Z.sub.n *.

대표청구항 ▼

[ I claim:] [1.] In a system for sending messages over a network between first and second computing units, a method comprising the following steps:(a) encrypting a message M into ciphertext C at the first computing unit, where the ciphertext C includes a value V and a value W, as follows:(1) the val

[ I claim:] [1.] In a system for sending messages over a network between first and second computing units, a method comprising the following steps:(a) encrypting a message M into ciphertext C at the first computing unit, where the ciphertext C includes a value V and a value W, as follows:(1) the value V is a function of a number x, V=x.sup.e, where e is an integer and x is as follows:x=g.sup.R mod n, where:(i) n is a number n=p.sub.1 p.sub.2 where p.sub.1 and p2 are prime numbers with p.sub.1 =r.sub.1 q.sub.1 +1 and p.sub.2 =r.sub.2 q.sub.2 +1, where r.sub.1 and r.sub.2 are random numbers, and q.sub.1 and q.sub.2 are prime numbers;(ii) R is a random number selected independent of the random numbers r.sub.1 and r.sub.2 ; and(iii) g is a number in the form of g=r.sub.3.sup.(p.sbsp.1.sup.-1)(p.sbsp.2.sup.-1)/(q.sbsp.1 .sup.q.sbsp.2.sup.) mod n, where r.sub.3 is a random number selected independent of the random numbers r.sub.1, r.sub.2, and R;(2) the value W is a function of a value h(x) and the message M, the value h(x) being a result of a one-way function of the number x;(b) sending the ciphertext C from the first computing unit to the second computing unit; and(c) decrypting the ciphertext C at the second computing unit to reproduce the message M, where M is a function of the value W and the value h(x) and x is derived as x=V.sup.(1/e) mod q.sbsp.1.sup.q.sbsp.2 mod n.