Patent ID: 8649508

Claim:
A method for using a computing device including a processor and a memory, the method for performing Elliptic curve scalar multiplication in cryptography comprising the following steps: (a) receiving, into the memory from a source external to the memory, a Double Base Number System (DBNS) sum; (b) computing, using the processor, R sum from the DBNS sum, wherein the computing of the R sum from the DBNS sum is performed separately and one at a time if the DBNS sum includes repeated exponents; and (c) determining, using the processor, a point nPεE(F), where E(F) is an elliptic curve over a prime/binary field F, wherein the DBNS sum includes a decreasing order of exponents, and wherein step (a) includes the step of receiving an input of integer n=Σfinite S 2 x 3 y =ΣS i 2 bi 3 bi , (i=1, 2, . . . , m) with s i ε {−1,1}, and such that b 1 b≧b 2≧ . . . ≧ b m ≧0, and t 1 ≧t 2 ≧ . . . ≧t m ≧0; and wherein step (c) includes the step of computing the values of u=b i −b i+1 and v=t i −t i+1 when the values of i are taken as 1, 2, . . . , m−1.