Abstract
The Diffie-Hellman key exchange algorithm can be implemented using the group of points on an elliptic curve over the field \( \mathbb{F}_{2^n } \) . A software version of this using n = 155 can be optimized to achieve computation rates that are slightly faster than non-elliptic curve versions with a similar level of security. The fast computation of reciprocals in \( \mathbb{F}_{2^n } \) is the key to the highly efficient implementation described here.
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This work was supported by the National Computer Security Center, contract MDA904-92-C-5151.
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Schroeppel, R., Orman, H., O’Malley, S., Spatscheck, O. (1995). Fast Key Exchange with Elliptic Curve Systems. In: Coppersmith, D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44750-4_4
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