Patent ID: 7904721

Claim:
A method for producing a certificate, the certificate comprising data, the method comprising: generating a modulus N by a computer programmed to generate the modulus N by a scattering method L, a function R and a seed s, where N is generated, in part, by scattering bits of R(s) throughout N using the scattering method L; and all bits of N other than R(s) are denoted by t; generating a key pair (E,D) by the computer, which is programmed to generate the key pair (E,D) such that E=F(s,t), D being a private key, E being a public key, F being a publicly known function; and producing the certificate, including the public key E in compressed form by the computer, which is programmed to include the s and the t in the certificate instead of the public key E, wherein the s and the t together are shorter than the E and, wherein the public key E is generable from the s and the t.