A method of generating and verifying a digital signature by selecting an elliptic curve; selecting a point G; generating x and M; reducing x; generating a base tau expansion, in non-adjacent form, of the reduced x; multiplying G by the expansion; computing h=Hash(M); generating k; reducing k; generating a base tau expansion, in non-adjacent form, of the reduced k; multiplying G by the expansion of k to form K=(K.sub.x,K.sub.y); computing R=(K.sub.x mod q); returning to the step of generating k if R=0, otherwise computing S=(k -1)(h+xR); returning to the step of generating k if S=0, otherwise transmitting y, q, M, R, and S; receiving y, q, M, R, and S; proceeding with the next step if 0<R<q and 0<S<q, otherwise not verifying the digital signature and stopping; forming h=Hash(M); computing f=((S -1) mod q), b=(hf mod q), and t=(Rf mod q); reducing b and t; generating a base tau expansion, in non-adjacent form, of the reduced b; multiplies G by the result of the last step to form a point B; reduces t; generates a base tau expansion, in non-adjacent form, of the reduced b and t; multiplying G by the expansion of t; computing V=B+T, where V=(V.sub.x,V.sub.y); computing v=(V.sub.x mod q); and verifying the digital signature if v=R, otherwise not verifying the digital signature.Method of elliptic curve cryptographic digital signature generation and verification using reduced base tau expansion in non-adjacent form624346705/06/200123/07/199820011,048Reiter; Robert W.Solinas; Jerome A.US Patent and Trademark OfficeGoogle Patent Searchpatentimages.storage.googleapis.com/US6243467B1/US06243467-20010605-D00000.pngUniquebase tau expansionnon-adjacent formdigital signaturemodexpansionelliptic curvedigital signature generationpointmethodhash