Reference Work Entry

Encyclopedia of Cryptography and Security

pp 879-879

# Nyberg–Rueppel Signature Scheme

• Kazue SakoAffiliated withNEC

## 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 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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