Patent ID: 7680271

Claim:
An asymmetrical key cryptography method involving a processor-implemented keyholder having a number m≧1 of private keys Q 1 , Q 2 , . . . , Q m and respective public keys G 1 , G 2 , . . . , G m , each pair of keys (Q i , G i ) (where i=1, . . . , m ) satisfying either the relationship G i =Q i v mod n or the relationship G i ×Q i v =1 mod n, where n is a public integer equal to the product of f(where f>1) private prime factors p 1 , . . . , p f , at least two of which are separate, and the exponent v is a public integer equal to a power of 2, wherein the method comprises: arranging, by a processor, exponent v to have the relationship v=2 b+k , where k is a strictly positive integer and b=max(b 1 , . . . , b f ), where b j (where j=1, . . . , f) is the highest integer such that (p j −1)/2 bj−1 is even; and arranging, by the processor each public key G i (where i=1, . . . , m ) to have the form G i =g i 2 a i , mod n, where the base numbers g i are integers strictly greater than 1 and the numbers a i , are integers such that 1≦a i , ≦b and at least one of them is strictly greater than 1.