A Schnorr group, proposed by Claus P. Schnorr, is a large prime-order subgroup, the p for some prime.

Definition

such that

until you find one such that

1. .

This value

.

Applications

Schnorr groups are useful in discrete log based cryptosystems including Schnorr signatures and DSA is chosen to be large enough to resist index calculus is large enough to resist the birthday attack on discrete log problems, which works in any group (perhaps 160 to 256 bits). Because the Schnorr group is of prime order, it has no non-trivial proper subgroups, thwarting confinement attacks is also a generator of the group.

References