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Schnorr signature

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In cryptography, a Schnorr signature is a digital signature produced by the Schnorr signature algorithm. Its security is based on the intractability of certain discrete logarithm problems. It is considered the simplest digital signature scheme to be provably secure in a random oracle model. It is efficient and generates short signatures. It is covered by Template:US patent, which expired in February 2008.

AlgorithmEdit

Choosing parametersEdit

Key generationEdit

  • Choose a private key x such that 0<x<q.
  • The public key is y where y = gx.

SigningEdit

To sign a message M:

  • Choose a random k such that 0<k<q
  • Let r=g^k\,
  • Let e=H(M||r),\, (where || denotes concatenation)
  • Let s=(k-xe) \;\text{mod } q

The signature is the pair (e,s). Note that 0 \le e < q and 0 \le s < q; if a Schnorr group is used and q < 2^{160}, then the signature can fit into 40 bytes.

VerifyingEdit

  • Let r_v=g^sy^e\,
  • Let e_v=H(M||r_v)\,

If e_v=e then the signature is verified.

Public elements: G,g,q,y,s,e,r. Private elements: k,x.

See alsoEdit

ReferencesEdit

  • C.P. Schnorr, Efficient identification and signatures for smart cards, in G. Brassard, ed. Advances in Cryptology—Crypto '89, 239-252, Springer-Verlag, 1990. Lecture Notes in Computer Science, nr 435
  • Claus-Peter Schnorr, Efficient Signature Generation by Smart Cards, J. Cryptology 4(3), pp161–174 (1991) (PS).
  • Menezes, Alfred J. et al. Handbook of Applied Cryptography CRC Press. 1996.
de:Schnorr-Signatur

fr:Protocole d'authentification de Schnorr ru:Схема Шнорра

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