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. We present fast and practical methods for generating randomlydistributed pairs of the form (x; gxmod p) or (x; xemod N ), usingprecomputation. These generation schemes are of wide applicabilityfor speeding-up public key systems that depend on exponentiation andoffer a smooth memory-speed trade-off. The steps involving exponentiationin these systems can be reduced significantly in many cases. Ourschemes are most suited for server applications. We present security analyses...

Speeding up discrete log and factoring based schemes via precomputations