Reliable elliptic curve cryptography computation

Abstract

A method for reliable computation of point additions and point multiplications in an elliptic curve cryptography (ECC) system. Two asymmetric operations are performed: one of the operations is of slightly higher complexity than a conventional ECC operation, and the other operation is of much lower complexity than the first operation. The complexity of the second operation is a function of the desired degree of reliability, or the desired probability of failure detection. The method validates a computation involving one or more points on a specified elliptic curve by selecting a second elliptic curve, deriving a third elliptic curve from the specified and selected curves, projecting points onto the derived curve, performing a computation on the derived curve involving the projected points, validating the computation on the selected curve, extracting from the computation on the derived curve a predicted result of the computation on the selected curve, and comparing the predicted result to the computation on the selected curve. A predicted result of the computation to be validated may then be extracted from the computation on the derived curve. The predicted result is compared to an actual result of a computation on the selected curve, and if the results match, the predicted result of the computation performed on the selected curve is validated.

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