Opposing to spy behavior, the converse modulo calculation conservation

摘要

In methods for determining, in a way that is protected against spying, the modular inverse b of a value a in relation to a module n for a cryptographic application, an auxiliary value beta and an auxiliary module delta are determined at least depending on the value a, the module n and at least one masking parameter r, an auxiliary inverse beta' is determined as the modular inverse of the auxiliary value beta in relation to the auxiliary module delta, and the modular inverse b is determined at least depending on the auxiliary inverse beta', the at least one masking parameter r, and the auxiliary value beta and/or the auxiliary module delta. A computer program product and a portable data carrier have corresponding features. The invention provides a method for modular inversion, secured against spying, which is suitable for applications where security is critical, such as, e.g. cryptographic calculations on a portable data carrier.