Patent ID: 10601578

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 p, 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(p) and isomorphic to an additive group (/r)+ through isomorphism γ; forming a combined group E(p)×′E(p)×(/r)+ which is isomorphic to a cross product of the groups E(p) and (/r)+; selecting an element  in /r and defining an element P′=γ() in group ′; forming a combined element {circumflex over (P)}=CRT(P,P′) in the group E(p)×′; calculating {circumflex over (Q)}=[k]{circumflex over (P)} in the combined group E(p)×′; calculating k in /r; and checking whether {circumflex over (Q)}≡Q′(mod r) where Q′=γ(k).