Speeding up Curve25519 using Toeplitz Matrix-vector Multiplication

Date

2018-01-24

Author

Taskin, Halil Kemal
Cenk, Murat

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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This paper proposes a new multiplication algorithm over F-2(255)-19 where the de-facto standard Curve25519 [2] algorithm is based on. Our algorithm for the underlying finite field multiplication exploits the Toeplitz matrix-vector multiplication and achieves salient results. We have used a new radix representation that is infeasible when used with schoolbook multiplication techniques but has notable advantages when used with Toeplitz matrix-vector multiplication methods. We present the new algorithm and discuss the comparison and implementation details. In addition, we evaluate the delay complexity of four-core almost embarrassingly parallel implementation of our algorithm when computations are performed using multi-core systems.

Subject Keywords

Elliptic curve cryptography, Toeplitz matrix-vector multiplication, curve25519

URI

https://hdl.handle.net/11511/31681

DOI

https://doi.org/10.1145/3178291.3178292

Collections

Graduate School of Applied Mathematics, Conference / Seminar

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Citation Formats

H. K. Taskin and M. Cenk, “Speeding up Curve25519 using Toeplitz Matrix-vector Multiplication,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31681.