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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 \emph{Curve5453} and \emph{Curve6071}, two Montgomery curves over the Crandall prime $2^{545}-3$ and Mersenne prime $2^{607}-1$, respectively, providing 271 and 302 bits of classical security. Comprehensive security analysis shows \emph{Curve6071} passes all verifiable \emph{SafeCurves} criteria while \emph{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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