Abstract: A computer hardware implemented cryptography method computes a modular exponentiation, M :=Cd (mod p·q), upon a message data value C using a Chinese Remainder Theorem (CRT) based technique. To secure against cryptanalysis, the private key moduli p and q are transformed by multiplication with a generated random value s, so that p?: =p·s and q? :=q·s, as shown in an exemplary embodiment in FIG. 2. The CRT steps of the modular exponentiation are applied using the transformed moduli p? and q? to obtain a random intermediate message data value M?. A final reduction of M? modulo p·q yields the final message data value M. Values needed for the computation are loaded into data storage and accessed as needed by electronic processing hardware.

Abstract: A computer hardware implemented cryptography method computes a modular exponentiation, M:=Cd (mod p·q) upon a message data value C using a Chinese Remainder Theorem (CRT) based technique. To secure against cryptanalysis,, the private key moduli p and q are transformed by multiplication with a generated random value s, so that p?:=p·s and q?:=q·s. The CRT steps of the modular exponentiation are applied using the transformed moduli p? and q? to obtain a random intermediate message data value M?. A final reduction of M? modulo p·q yields the final message data value M. Values needed for the computation are loaded into data storage and accessed as needed by electronic processing hardware.