Patent ID: 8280041

Claim:
A cryptographic method implemented in an electronic processing system for performing modular exponentiation computations, comprising: loading private key values, including at least one private key exponent and two private key moduli p and q, wherein the two private key moduli are p and q, into a data storage accessible to electronic processing hardware; selecting, by the electronic processing hardware, a non-random pre modular exponentiation transformation factor to secure cryptographic operations utilizing modular exponentiation from cryptanalysis, wherein the transformation factor is co-prime with the private key moduli; multiplying, by the electronic processing hardware, the private key moduli by the transformation factor to produce transformed moduli p′ :=p·s and q′ :=q·s, wherein the transformed moduli are p′ and q′ and wherein the transformation factor is s; loading a first data value into the data storage at any time prior to performing modular exponentiation; computing, by the electronic processing hardware, at least one transformed inverse value, R′ :=(p′) −1 (mod q); performing, by the electronic processing hardware, a modular exponentiation upon the first data value using the at least one private key exponent and the transformed moduli to obtain an intermediate data value; and reducing, by the electronic processing hardware, the intermediate data value modulo a product of the two private key moduli to obtain a final data value.