Secure Montgomery curves over Toeplitz matrix-vector product friendly primes for high-performance elliptic curve cryptography

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.