An Entropy Leakage Algebra for IEEE 754 Floating-Point Cryptographic Computations

doi:10.26565/2304-6201-2026-69-06

Taras Starushenko National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37 Beresteiskyi Ave., Kyiv, 03056, Ukraine https://orcid.org/0009-0008-9226-4666

DOI: https://doi.org/10.26565/2304-6201-2026-69-06

Keywords: : entropy leakage algebra, semiring, IEEE 754 arithmetic, cryptographic entropy, floating-point nondeterminism, compositional security, min-entropy, post-quantum cryptography

Abstract

Relevance. Floating-point arithmetic is not neutral ground for cryptography. The IEEE 754 standard leaves enough room for hardware and compilers to vary—in rounding, in FMA contraction, in subnormal handling—that the same program can produce measurably different intermediate distributions depending on where it runs. This nondeterminism is invisible to the programmer yet can shift probability mass in secret-dependent distributions, creating entropy leakage risks unaccounted for by conventional security models.

Objective. To develop a rigorous compositional framework—the Entropy Leakage Algebra (ELA)—for bounding the min-entropy loss induced by IEEE 754 floating-point arithmetic across arbitrarily complex cryptographic pipelines.

Methods. The ELA is a commutative semiring whose elements are symbolic leakage expressions. Two operations—⊕ for sequential composition and ⊗ for parallel branching—reflect the structure of floating-point pipeline execution. Four generator families grounded in IEEE 754 semantics (directed rounding γρ, FMA contraction γf, flush-to-zero γz, and expression reordering γr) are defined and proved sound via min-entropy bounds.

Results. The semiring axioms are proved. A unique Sum-of-Maxima Normal Form (SMNF) is established, computable in O(|e|²). The domination order on elements is shown to be decidable in polynomial time, enabling automated platform comparison. Three case studies—an ML-KEM NTT pipeline (8.6 vs. 8.3 bits empirical), an RSA Montgomery ladder (12.7 bits exact match), and a neural-network key-derivation function (4.8 vs. 4.75 bits)—validate algebraic bounds against empirical measurements with agreement within 4%.

Conclusions. The ELA provides a mechanizable certification path for entropy safety of floating-point cryptographic implementations. The SMNF analysis identifies flush-to-zero subnormal handling (γz) as the dominant vulnerability across all studied pipelines, a structural result that would otherwise require separate empirical measurement campaigns.

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Author Biography

Taras Starushenko, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", 37 Beresteiskyi Ave., Kyiv, 03056, Ukraine

PhD student, Department of Information Security

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