Protecting ecc against fault attacks

Abstract

A method for protecting against faults in a computation of a point multiplication Q=[k]P on an elliptic curve E defined over a prime field, including: defining an integer r and a group'={γ()|∈/r} represented with elements having a group law that coincides with a group law used in the representation for E() and isomorphic to an additive group (/r)through isomorphism γ; forming a combined group E()×′E()×(/r)which is isomorphic to a cross product of the groups E() and (/r); selecting an elementin/rand defining an element P′=γ() in group′; forming a combined element {circumflex over (P)}=CRT(P,P′) in the group E()×′; calculating {circumflex over (Q)}=[k]{circumflex over (P)} in the combined group E()×′; calculating kin/r; and checking whether {circumflex over (Q)}≡Q′(mod r) where Q′=γ(k).