Accelerated verification of digital signatures and public keys

Accelerated computation of combinations of group operations in a finite field is provided by arranging for at least one of the operands to have a relatively small bit length. In a elliptic curve group, verification that a value representative of a point R corresponds the sum of two other points uGand vG is obtained by deriving integers w, z of reduced bit length and so that v = w/z. The verification equality R = uG + vQ may then be computed as -zR + (uz mod nG + wQ = O with z and w of reduced bit length. This is beneficial in digital signature verification where increased verification can be attained.