A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.
Elliptic curve cryptosystems
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A new multi-surface evidence framework for post-quantum TLS observability that combines passive, active, certificate, and registry data to assess endpoint capabilities across TLS 1.2/1.3 scenarios and outperforms prior analyzers in controlled tests and public campaigns.
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Space-Efficient Quantum Algorithm for Elliptic Curve Discrete Logarithms with Resource Estimation
A space-efficient quantum ECDLP algorithm uses 5n + 4⌊log₂n⌋ + O(1) logical qubits and O(n³) Toffoli gates, lowering the 256-bit estimate from 2124 to 1333 qubits.
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Observability for Post-Quantum TLS Readiness: A Multi-Surface Evidence Framework
A new multi-surface evidence framework for post-quantum TLS observability that combines passive, active, certificate, and registry data to assess endpoint capabilities across TLS 1.2/1.3 scenarios and outperforms prior analyzers in controlled tests and public campaigns.