Patent ID: 8457309

Claim:
An apparatus to derive a private cryptographic key having a complementary public cryptographic key, the private cryptographic key including a modulus and a private exponent, the apparatus comprising: a non-volatile memory to store a number, an indication of the modulus, and an indication of a multiplicative factor, wherein: the number is shorter than the private exponent of the private cryptographic key; the private exponent comprises an upper part and a lower part, the lower part being the least significant bits of the private exponent, the upper part being the bits of the private exponent excluding the lower part; and the number stored in the memory is indicative of the lower part of the private exponent; and a processor, which is configured to receive an instruction indicating that the private cryptographic key is to be applied to data and, responsively to the instruction, to compute the private cryptographic key and to perform a cryptographic operation on the data using the private cryptographic key, wherein the processor is configured to compute the private exponent by: computing the lower part of the private exponent using the stored number; computing the upper part of the private exponent using the modulus, the public exponent and the multiplicative factor; and concatenating the calculated upper part with the lower part.