Arithmetic for Large-Characteristic Finite Fields in CKKS ⋆

High-Precision Homomorphic ALU over Arbitrary Moduli with O (1) Bootstrapping

Provable Subexponential Algorithms for NIST Third-Round Lattice Families

We give provable classical subexponential algorithms for secret recovery in growing parameter families associated with NIST third-round lattice candidates. For the Kyber/ML-KEM, FrodoKEM, SABER, NTRU LPRime, and Dilithium/ML-DSA families studied here, polynomial moduli and polylogarithmic coefficient scales yield recov...

Faster Post-Quantum zkSNARK Provers Using the LCH Polynomial Basis

Compressed Permutation Oracles Revisited

The compressed permutation oracle has been used to analyze the quantum security of a number of cryptographic constructions which resisted prior techniques. However, these analyses were fundamentally limited by the poor soundness of the method: the technique was proven sound only up to $O(N^{1/12})$ queries to permutati...

Polynomial Evaluation on Many Inputs with Bounded Hamming Weight over GF(2)

Two-Sided Product Expanding Codes via Rademacher Matrices

We give a proof of the existence of two-sided product expanding codes which, unlike the earlier result of Kalachev and Panteleev (FOCS, 2025), does not rely on explicit constructions of asymptotically optimal locally testable codes ($c^3$-LTCs). For every fixed number of component codes and dimensions whose rates are b...