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On equivalence between known families of quadratic APN functions
CCZ-equivalence EA-equivalence APN
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2019/7/15
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...
On the Distribution of Quadratic Residues and Non-residues Modulo Composite Integers and Applications to Cryptography
Jacobi symbol probability distribution statistical distance
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2019/6/4
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...
On the boomerang uniformity of quadratic permutations over $\mathbb{F}_{2^n}$
Vectorial functions Block ciphers Boomerang uniformity
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2019/3/13
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 ...
Correlation of Quadratic Boolean Functions: Cryptanalysis of All Versions of Full MORUS
Quadratic Boolean function Disjoint quadratic form Correlation attack
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2019/3/1
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...
Shorter Quadratic QA-NIZK Proofs
zero knowledge elliptic curve cryptosystem
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2019/3/1
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...
Decentralized Evaluation of Quadratic Polynomials on Encrypted Data
Decentralization FHE 2-DNF
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2018/11/2
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...
Classification of Balanced Quadratic Functions
Affine Equivalence S-box Boolean functions
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2018/2/1
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...
Fast Quantum Algorithm for Solving Multivariate Quadratic Equations
NSA Solving Multivariate Quadratic Equations
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2017/12/25
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
FXL Grover reversibility
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2017/12/19
Asymptotically faster quantum algorithms to solve multivariate quadratic equations.
Practical Functional Encryption for Quadratic Functions with Applications to Predicate Encryption
functional encryption predicate encryption
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2017/2/23
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 ...
Some Results on the Known Classes of Quadratic APN Functions
APN function quadratic function Walsh spectrum
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2017/1/3
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...
Generic Zero-Knowledge and Multivariate Quadratic Systems
zero-knowledge proof post-quantum signature
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2016/12/29
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 ...
Functional Encryption for Quadratic Functions, and Applications to Predicate Encryption
functional encryption quadratic functions predicate encryption
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2016/12/7
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...
Software implementation of Koblitz curves over quadratic fields
landmark paper Software implementation
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2016/6/12
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 Quadratic Equations with XL on Parallel Architectures - extended version
block Wiedemann sparse solver multivariate quadratic systems
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2016/5/3
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...