A survey of fast exponentiation methods
Journal of Algorithms
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
Algorithms for Multi-exponentiation
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Analysis of Fractional Window Recoding Methods and Their Application to Elliptic Curve Cryptosystems
IEEE Transactions on Computers
Improved techniques for fast exponentiation
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
A note on the signed sliding window integer recoding and a left-to-right analogue
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
New minimal weight representations for left-to-right window methods
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Fractional windows revisited: improved signed-digit representations for efficient exponentiation
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
Accelerated verification of ECDSA signatures
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
A New Variant of the Cramer-Shoup KEM Secure against Chosen Ciphertext Attack
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Efficient leakage-resilient public key encryption from DDH assumption
Cluster Computing
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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 g2, ..., gkare fixed while g1is 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 g1where, besides obtaining the actual result, we create a cache entry based on g1, investing very little memory or time overhead.The second way applies to any multi-exponentiation once such a cache entry exists for the g1in question and provides for a significant speed-up.