Fault-resistant calculcations on elliptic curves

摘要

Means for checking the correctness of a cryptographic operation on an elliptic curve E (Z/ p Z) , including fault-resistant computation of Q = kP on elliptic curve E (Z/ p Z). Elliptic curve E^ (Z/ pr 2 Z) ‰¡ E (Z/ p Z) x E (Z/ r 2 Z) is given (110) by Chinese remaindering and where r is an integer. A point P ^ = CRT( P (mod p ), R (mod r 2 )) is formed (120) in E^ (Z/ pr 2 Z); P ^ reduces to P in E (Z/ p Z) , and to R in E 1 (Z/r 2 Z). Q ^ = kP^ in E^ (Z/ p r 2 Z) is computed (130). It is then verified (140) whether Q ^ ‰¡ kR (mod r 2 ) in E 1 (Z/ r 2 Z), and if so, Q = Q ^ mod p is output, whereas "error" is returned if this is not the case. Also provided are an apparatus (200) and a computer program product (240).