Arithmetic of Finite Fields
Description
This book constitutes the refereed proceedings of the 11th International Workshop on Arithmetic of Finite Fields, WAIFI 2026, held in Santander, Spain, during June 3-5, 2026.
The 21 full papers and 3 Invited papers included in this book were carefully reviewed and selected from 31 submissions. They were organized in topical sections as follows: Invited talks; Coding Theory and Related Structures; Cryptography and Boolean Functions; Finite Field Arithmetic, Algorithms, and Implementations; and Combinatorics, Curves, and Dynamical Structures.
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Content
.- Invited Talks.
.- New invariants for rank metric codes, with applications to the classification of rank two semifields of order.
.- A Survey on Code Equivalence: The State-of-the-Art and Open Questions.
.- Eidolon: A Post-Quantum Signature Scheme Based on k-Colorability in the Age of Graph Neural Networks.
.- Coding Theory and Related Structures.
.- Output feedback transformations for preserving observability and structural decodability in convolutional codes.
.- The Non-Asymptotic Landscape of Abelian Codes: A Framework for (F,G) Goodness.
.- Algebraic geometry codes with many automorphisms arising from Galois points.
.- Classification of Hermitian-relative curves up to projective equivalence.
.- Improvements to Jacobian Arithmetic in Global Function Fields.
.- On Secret Sharing from Extended Norm-Trace Curves.
.- Self-Orthogonal Codes from p-ary Quadratic Forms via Character Sums with Applications to LCD and Arbitrary Hull Dimensional Codes.
.- Cryptography and Boolean Functions.
.- On the (Non-)Existence of Efficient Class Group Orbits for Collision Search in CSIDH.
.- A new construction of locally-APN functions on F_2^{2m} using spreads and Sidon sets.
.- On the Resilience Order of Weightwise Almost Perfectly Balanced Functions.
.- A notion on S-boxes for a partial resistance to some integral attacks.
.- Boolean Arithmetic over F_2 from Group Commutators.
.- Finite Field Arithmetic, Algorithms, and Implementations.
.- Equality Tests in the Polynomial Modular Number System.
.- Period Counting versus Direct Sampling in Oscillator-based TRNGs: Architectures and Characteristics.
.- On the Feasibility of 256-bit Prime Field Arithmetic via PMNS on 8-bit Architectures.
.- Fast and Energy-Efficient Polynomial Multiplication using FFT, FFNT, and NTT on GPUs for Fully Homomorphic Encryption.
.- From Compact to Fast: Exploring 32- and 64-Bit AES Datapaths for IoT Systems.
.- Combinatorics, Curves, and Dynamical Structures.
.- Constructing a parameterized polynomial map through functional graphs and applications.
.- Codegrees and an Exact Triangle Formula for the Norm-One Cayley Graph over F_{q^3} in Characteristics.
.- Explicit Bounds on the Existence Probability of Random Multivariate Quadratic Systems over Finite Fields.
.- Automorphism groups of hyperelliptic curves of 2-rank zero.