Tailored Limb Counts, Faster Arithmetic: Improved TMVP Decompositions for Curve5453 and Curve6071

Date

2027-01-01

Author

Cenk, Murat
Kilic, N. Gamze Orhon
Taskim, Halil Kemal
Yayla, Oğuz

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Curve5453 and Curve6071 are Montgomery curves over the primes 2(545) -3 and 2(607) -1, providing 271- and 302-bit classical security, respectively. Their TMVP-based field multiplication in 10-limb representation costs 77 multiplications. We reduce this to 60 for Curve5453 (22% fewer) using a 9-limb radix-2(61) representation, and to 54 for Curve6071 (30% fewer) using a 12 -limb radix-2(5)1 representation with hierarchical block-level TMVP. Choosing the limb count to produce 3 x 3 Toeplitz blocks aligns the structure with the size-3 TMVP formula, computing each block product in 6 multiplications rather than 9. Portable C implementations benchmarked on ARM64 and x86-64 confirm speedups of up to 16% in field multiplication and 13% in scalar multiplication. On ARM64, Curve5453 reaches 90.6% of OpenSSL's assembly-optimized NIST P-521 ECDH throughput with 12 additional bits of classical security, and Curve6071 delivers 302-bit classical security at 80.8% of P-521's throughput.

URI

https://hdl.handle.net/11511/120872

DOI

https://doi.org/10.1007/978-3-032-29251-3_9

Conference Name

19th International Conference on Computational Intelligence in Security for Information Systems-CISIS

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Citation Formats

M. Cenk, N. G. O. Kilic, H. K. Taskim, and O. Yayla, “Tailored Limb Counts, Faster Arithmetic: Improved TMVP Decompositions for Curve5453 and Curve6071,” Marbella, İspanya, 2027, vol. 3013, Accessed: 00, 2026. [Online]. Available: https://hdl.handle.net/11511/120872.