Framework measures cryptographic security across diverse adversary costs
GAUGE: A Formal Framework for Measuring Cryptographic Security under Heterogeneous Adversary Cost Models
Cryptography and Security
Summary
Cryptographic security is often reported as a single number, but this number depends on how you measure the attacker’s resources like time, memory, or quantum power. The authors propose GAUGE, a system that treats security as a curve based on different ways to value these resources, making it easier to compare schemes fairly. Their method can detect when rankings of cryptographic methods change based on assumptions and precisely explains why. GAUGE also estimates risks combining uncertainty about attacker cost and how attacks get easier over time.
What this means in practice
- •For cryptographic standards bodies: Certify and communicate robust security rankings that remain valid across different attacker cost assumptions using GAUGE’s formal framework.
- •For security architects: Evaluate and choose cryptographic schemes with explicit insight into how cost model changes affect security comparisons and hybrid protocol design.
Authors
Bhanwar Gupta, Sanjeev Rana
Abstract
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.