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We study a question whether the currently known families of quadratic APN polynomials are pairwise different up to CCZ-equivalence. We reduce the list of these families to those CCZ-inequivalent to ea...
We develop exact formulas for the distribution of quadratic residues and non-residues in sets of the form a+X={(a+x)modn∣x∈X}a+X={(a+x)modn∣x∈X}, where nn is a prime or the product of two primes and X...
At Eurocrypt'18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new tool called Boomerang Connectivity Table (BCT) for measuring the resistance of a block cipher against the boomerang attack which ...
We show that the correlation of any quadratic Boolean function can be read out from its so-called disjoint quadratic form. We further propose a polynomial-time algorithm that can transform an arbitrar...
Despite recent advances in the area of pairing-friendly Non-Interactive Zero-Knowledge proofs, there have not been many efficiency improvements in constructing arguments of satisfiability of quadratic...
Machine learning and group testing are quite useful methods for many different fields such as finance, banks, biology, medicine, etc. These application domains use quite sensitive data, and huge amoun...
S-boxes, typically the only nonlinear part of a block cipher, are the heart of symmetric cryptographic primitives. They significantly impact the cryptographic strength and the implementation character...
In August 2015 the cryptographic world was shaken by a sudden and surprising announcement by the US National Security Agency (NSA) concerning plans to transition to post-quantum algorithms. Since this...
Asymptotically faster quantum algorithms to solve multivariate quadratic equations.
We present two practically efficient functional encryption schemes for a large class of quadratic functionalities. Specifically, our constructions enable the computation of so-called bilinear maps on ...
In this paper, we determine the Walsh spectra of three classes of quadratic APN functions and we prove that the class of quadratic trinomial APN functions constructed by G\"olo\u glu is affine equival...
Zero-knowledge proofs are a core building block for a broad range of cryptographic protocols. This paper introduces a generic zero-knowledge proof system capable of proving the correct computation of ...
We present a functional encryption scheme based on standard assumptions where ciphertexts are associated with a tuple of values (x 1 ,...,x n ) in Z p n, secret keys are associated with a degree-two p...
In this work, we retake an old idea that Koblitz presented in his landmark paper, where he suggested the possibility of defining anomalous elliptic curves over the base field \F_4. We present a carefu...
Solving a system of multivariate quadratic equations (MQ) is an NP-complete problem whose complexity estimates are relevant to many cryptographic scenarios. In some cases it is required in the best kn...

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