Reference Work Entry

Encyclopedia of Cryptography and Security

pp 879-879

Nyberg–Rueppel Signature Scheme

  • Kazue SakoAffiliated withNEC

Related Concepts

Digital Signature Schemes; Discrete Logarithm Problem


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.


The following gives a typical interpretation of the Nyberg–Rueppel signature scheme:
  • Key generation: a prime numberp, a prime factor q of p − 1, an element g of orderq in the group of integers modulo p, and a secret key x(0 < x < q). The public key consists of p,  q,  g, and \(y = {g}^{x}\textrm{ mod}\,p\) (modular arithmetic).

  • Signing: for message m, compute \(r = m \cdot {g}^{k}\ \textrm{ mod}\ p,\ \acute{\textrm{ r}} = r\) mod \(q,\ s = -k - {r}^{{\prime}}\cdot x\) mod q, and output (r, s). Verification: verify s < q, compute \({r}^{{\prime}} = r\) mod q, and check that \({g}^{s} \cdot {y}^{{r}^{{\prime}} }\cdot r = m\).

From the construction, it is clear that if a valid signature (r, s) for m is given, then ...

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