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Secure Montgomery curves over TMVP-friendly primes for high-performance ECC

algorithms-and-analysis-of-algorithms
cryptography
security-and-privacy
quantum-computing
blockchain

Abstract

We propose Curve5453 and Curve6071, two Montgomery curves over the Crandall prime 545 and Mersenne prime 607, respectively, providing 271 and 302 bits of classical security. Comprehensive security analysis shows Curve6071 passes all verifiable SafeCurves criteria, while Curve5453 passes all except completeness. We develop TMVP-optimized field multiplication tailored to the arithmetic structure of these primes for 10-limb representations on 64-bit architectures, achieving 12.0% and 20.4% speedups over the closest alternative. ARM64 benchmarks show scalar multiplication completing in 871,898 and 895,028 cycles, respectively, competitive with existing lower-security alternatives such as E-521 (259-bit security) 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 SafeCurves-compliant alternatives beyond 260 bits with demonstrated practical performance on modern architectures.
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