Secure Montgomery curves over Toeplitz matrix-vector product friendly primes for high-performance elliptic curve cryptography
PeerJ Computer Science, cilt.12, sa.10, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 12 Sayı: 10
- Basım Tarihi: 2026
- Doi Numarası: 10.7717/peerj-cs.4095
- Dergi Adı: PeerJ Computer Science
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, Directory of Open Access Journals, Technology Collection (ProQuest)
- Anahtar Kelimeler: Elliptic curve cryptography, Fast arithmetic, High security, New curve, Toeplitz matrix-vector product
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
We propose Curve5453 and Curve6071, two Montgomery curves over the Crandall prime 2^545 - 3 and Mersenne prime 2^607 - 1, providing 271 and 302 bits of classical security, respectively. Comprehensive security analysis shows Curve6071 passes all verifiable SafeCurves criteria while Curve5453 passes all except completeness. We develop Toeplitz Matrix-Vector Product (TMVP)-optimized field multiplication tailored to the arithmetic structure of these primes for 10-limb representations on 64-bit architectures, achieving 12.0 and 19.6 speedups over the closest alternative. Benchmarks on a 64-bit Advanced RISC Machines (ARM64) platform show scalar multiplication completing in 871,898 and 903,542 cycles, respectively; we additionally report x86-64 (Intel i7-8565U) results and a same-platform Elliptic Curve Diffie-Hellman (ECDH) throughput comparison showing our curves achieve approximately 79 - 81 of the National Institute of Standards and Technology (NIST) P-521 throughput on ARM64 while delivering higher security levels. These curves address a critical gap for hybrid post-quantum constructions requiring classical security commensurate with quantum-resistant components, blockchain systems with decades-long security requirements, and specialized deployments where implementation robustness and enhanced classical security are essential, providing the first high-security Montgomery-form curves beyond 260 bits to meet these SafeCurves criteria, with demonstrated practical performance on modern architectures.