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access icon free Efficient elliptic curve Diffie-Hellman computation at the 256-bit security level

In this study, the authors introduce new Montgomery and Edwards form elliptic curves targeted at the 256-bit security level. To this end, they work with three primes, namely , and . While has been considered earlier in the literature, and are new. They define a pair of birationally equivalent Montgomery and Edwards form curves over all the three primes. Efficient 64-bit assembly implementations targeted at Skylake and later generation Intel processors have been made for the shared secret computation phase of the Diffie-Hellman key agreement protocol for the new Montgomery curves. Curve448 of the Transport Layer Security, Version 1.3 is a Montgomery curve which provides security at the 224-bit security level. Compared to the best publicly available 64-bit implementation of Curve448, the new Montgomery curve over leads to a 3–4% slowdown and the new Montgomery curve over leads to a 4.5–5% slowdown; on the other hand, 29 and 30.5 extra bits of security, respectively, are gained. For designers aiming for the 256-bit security level, the new curves over and provide an acceptable trade-off between security and efficiency.

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