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

Abstract

When verifying digital signatures, achieving a high throughput can be crucial. We present a technique that is useful for ECDSA and DSA signatures. It assumes that common domain parameters are used (which is typical of ECDSA) and that at least some signers recur (as in many application scenarios). We can achieve noticeable speedups in very different environments— from highly restricted ones where memory is very scarce to larger machines without severe memory restrictions. Requirements for the target platform are very small for a beneficial application of our technique. This makes it attractive for embedded systems, where ECDSA is a signature scheme of choice.

More generally, what we consider is 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 product. 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 and provides for a significant speed-up.