Tailored Limb Counts, Faster Arithmetic: Improved TMVP Decompositions for Curve5453 and Curve6071
19th International Conference on Computational Intelligence in Security for Information Systems-CISIS, Marbella, İspanya, 18 - 19 Haziran 2026, cilt.3013, ss.104-116, (Tam Metin Bildiri)
- Yayın Türü: Bildiri / Tam Metin Bildiri
- Cilt numarası: 3013
- Doi Numarası: 10.1007/978-3-032-29251-3_9
- Basıldığı Şehir: Marbella
- Basıldığı Ülke: İspanya
- Sayfa Sayıları: ss.104-116
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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.