Nyberg–Rueppel Signature Scheme

Related Concepts

Digital Signature Schemes; Discrete Logarithm Problem

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 $y = {g}^{x}\textrm{ mod}\,p$ (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 \((r,s + t\ \textrm{...