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Nyberg-Rueppel Signature Scheme

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Definition

Nyberg-Rueppel Signature Scheme is a signature scheme proposed in the paper "Message recovery for signature schemes based on the discrete logarithm problem" in 1995.

Theory

The following gives a typical interpretation of the Nyberg-Rueppel signature scheme:
  • Key generation: a prime number p, a prime factor q of p − 1, an element g of order q in the group of integers modulo p, and a secret key x(0 < x < q). The public key consists of p, q, g, and y = gxmod p (modular arithmetic).
  • Signing: for message m, compute mod q, s =  − k − r′⋅x mod q, and output (r, s). Verification: verify s < q, compute r′ = r mod q, and check that gs⋅yr′⋅r = m.

From the construction, it is clear that


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