Two 50% duty cycle divide-by-3 prescalers-sample-sample-hold (SSH) and sample-hold-hold (SHH) prescalers-in the 2 mm GaInP=GaAs heterojunction bipolar transistor (HBT) technology are realised. Current switchable emitter couple logic D flip-flops are employed to form both prescalers. The proposed SHH prescaler functions up to 2.6 GHz while the SSH prescaler operates from DC to 1.75 GHz. The maximum operating frequency of the SHH prescaler is enhanced about 50% compared with that of the SSH prescaler owing to better signal synchronisation.

tion rmx = k+s mod O@) and signature verification y'" = ra' mod p) , only the legitimate signer with knowledge of x can generate the signatures to satisfy the verification. Although the attacker can generate bogus signatures in the signature collection protocol, these signatures cannot satisfy the batch verification criterion. There are some other secure ElGamal type signature schemes as proposed in [4] that can also be used to design similar DSA type secure interactive batch verification protocols. We list those schemes in Table 1. Table 1: Secure ElGamal type signature schemes Signature Signature verification y"=r'a' mod 0 p y ' = r w n mod 0 p y'=ra"' mod 0 p sx=rk+m mod 0@) sx=k+mr mod 0@) (4) (r+m)x=k+s mod 0@) y'+"=ra' mod 0 p (5) sx=k+(m+r) mod 0 (p) y'=ra"'*' mod 0 p Conclusion: Instead of using an insecure batch verification criterion as proposed by the Naccache et al. in Eurocrypt '94, we propose several secure batch verification criteria in this Letter. By using the interactive batch verification protocol, the signer follows the signature collection protocol to generate n signatures through interactions with the verifier and the verifier validates all these n signatures at once through the batch verification criterion.

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