Electrical computers and digital processing systems: support – Multiple computer communication using cryptography – Particular communication authentication technique
Reexamination Certificate
2006-04-04
2006-04-04
Peeso, Thomas R. (Department: 2132)
Electrical computers and digital processing systems: support
Multiple computer communication using cryptography
Particular communication authentication technique
C713S182000, C713S152000, C713S152000
Reexamination Certificate
active
07024559
ABSTRACT:
A method of generating and verifying a cryptographic digital signature using joint sparse expansion by a signer first selecting a field, an elliptic curve over the field, a point P of order q on the elliptic curve, w, k. Next, generating W=wP and K=kP. Next, transforming K to K*. Next, combining K*, W, and a message M to produce h. Next, combining K*, W, and M to produce c. Next, generating, s by either s=hw+ck (mod q), s=(hw+c)/k (mod q), or s=(hk+c)/w (mod q). Next, forming the digital signature as (K*,s). Next, a verifier acquires the field, the elliptic curve, P, W, M, and (K*,s). Next, computing h and c. Next, selecting (n0, n1) as either (sc−1(mod q), −hc−1(mod q)), (cs−1(mod q), hs−1(mod q)) or (−ch−1(mod q), sh−1(mod q)). Next, generating binary expansions of n0and n1in joint sparse form. Next, computing, Q=n0P+n1W via twin multiplication and a double-add-subtract method with the binary expansions in joint sparse form. Next, transforming, Q to Q*. Lastly, verifying, the digital signature if Q*=K*.
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Morelli Robert D.
Peeso Thomas R.
The United States of America as represented by the National Secu
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