GAUGE: A Formal Framework for Measuring Cryptographic Security under Heterogeneous Adversary Cost Models
GAUGE frames cryptographic security as profiles over adversary cost models, certifying a ranking reversal between ML-KEM-512 and AES-128 from a 4–5% memory pricing shift.
GAUGE represents cryptographic security as a function over admissible adversary cost models (a security profile), proves profiles are piecewise-linear and concave, and establishes a rating trilemma when two profiles cross. A polynomial-time linear-programming procedure certifies whether the ranking of two schemes is robust, reverses under admissible models, or is genuinely incomparable. Applied to NIST post-quantum standards, the framework certifies a ML-KEM-512 versus AES-128 ranking reversal from a 4–5% shift in memory pricing and measures lattice-sieving cost drift of 9.79 bits per year over eight years. A hybrid X25519 + ML-KEM-768 handshake reduces combined-break probability twenty-fold at a 2.3 kilobyte cost.
- Security profiles over adversary cost models replace single bit-security numbers
- LP procedure certifies robust, reversed, or incomparable scheme rankings
- ML-KEM-512 vs AES-128 ranking reverses under 4–5% memory pricing shift
- Lattice-sieving costs drift 9.79 bits per year over eight years
- Hybrid X25519 + ML-KEM-768 cuts combined-break probability 20x for 2.3 KB
Full article251 words · extracted from arxiv.org · click to collapse
Standards bodies report cryptographic security as a single number of bits, but this value depends on the adversary cost model used to price time, memory, and quantum resources. Different conventions can therefore produce different rankings of cryptographic schemes. GAUGE represents security as a function over admissible cost models, called a security profile. Comparisons then become comparisons between profiles, and ranking reversals become an explicit structural property rather than a measurement error. We formalize price functionals over a cone of adversary cost models, show that security profiles are piecewise-linear and concave, and prove a rating trilemma: when two profiles cross, no rating can simultaneously be faithful to underlying costs, total over comparable pairs, and independent of the chosen cost model. We provide a polynomial-time linear-programming procedure that certifies whether the ranking of two schemes is robust, reverses under admissible models, or is genuinely incomparable. We extend GAUGE with a two-layer risk measure combining stochastic cryptanalytic decay with uncertainty over the appropriate cost model. We evaluate the framework on NIST post-quantum standards, classical anchors, and a 25-year chronology of cryptanalytic breaks. The analysis certifies a ranking reversal for ML-KEM-512 versus AES-128 from a 4-5% shift in memory pricing, and measures a lattice-sieving cost drift of 9.79 bits per year over eight years. A hybrid X25519 + ML-KEM-768 handshake reduces combined-break probability twenty-fold at a 2.3 kilobyte cost. The artifact reproduces all tables and figures in under seven seconds. GAUGE provides an explicit and auditable framework for reporting cryptographic security under competing cost models.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.17281