## Public Key Cryptography with a Group of Unknown Order

197. R. P. Brent,
* Public Key Cryptography with a Group of Unknown Order*,
Report PRG-TR-02-00, Oxford University Computing Laboratory,
5 June 2000, 11 pp.
Report:
dvi (20K),
pdf (165K),
ps (85K).

## Abstract

We present algorithms for digital signature generation and verification
using public key cryptography over an arbitrary group *G*.
The algorithms are similar to those of ElGamal,
but do not require a knowledge of the group order.
Forging signatures or determining the secret key
requires the solution of a discrete logarithm problem over *G*,
or the solution of other problems which appear at least as difficult.
The algorithms can be modified to work over arbitrary semigroups.
## Comments

The result
that point counting can be avoided at the cost of a protocol slowdown
was obtained independently by
J. S. Coron *et al*
[*ECC: Do we need to count ?*,
Proc. Asiacrypt 99, LNCS 1716, 122-134].
I thank John Pollard
for drawing Coron's paper to my attention.

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