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**2007/470**

**Title:**

Faster Multi-Exponentiation through Caching: Accelerating (EC)DSA Signature Verification

**Authors:**
Bodo Möller, Andy Rupp

**Abstract:**

We consider the task of computing power products \prod_{1 \leq i \leq k} g_i^{e_i} (“multi-exponentiation”) where base elements g_2, ..., g_k are fixed while g_1 is variable between multi-exponentiations but may repeat, and where the exponents are bounded (e.g., in a finite group). We present a new technique that entails two different ways of computing such a result. The first way applies to the first occurrence of any g_1 where, besides obtaining the actual result, we create a cache entry based on g_1, investing very little memory or time overhead. The second way applies to any multi-exponentiation once such a cache entry exists for the g_1 in question: the cache entry provides for a significant speed-up. Our technique is useful for ECDSA or DSA signature verification with common domain parameters and recurring signers.

**ePrint:**
https://eprint.iacr.org/2007/470

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