Provably secure distributed Schnorr signatures and a (t, n) threshold scheme for implicit certificates

In a (t, n) threshold digital signature scheme, t out of n signers must co-operate to issue a signature. We present an efficient and robust (t, n) threshold version of Schnorr's signature scheme. We prove it to be as secure as Schnorr's signature scheme, i.e., existentially unforgeable under adaptively chosen message attacks. The signature scheme is then incorporated into a (t,n) threshold scheme for implicit certificates. We prove the implicit certificate scheme to be as secure as the distributed Schnorr signature scheme.