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How to leverage hardness of constant degree expanding polynomials over R to build iO
public-key cryptography Obfuscation
2019/9/16
In this work, we introduce and construct DD-restricted Functional Encryption (FE) for any constant D≥3D≥3, based only on the SXDH assumption over bilinear groups. This generalizes the notion of 33-res...
There Are 10 Types of Vectors (and Polynomials): Efficient Zero-Knowledge Proofs of "One-Hotness" via Polynomials with One Zero
Zero-knowledge efficiency privacy-preserving protocols
2019/8/30
We present a new 4-move special honest-verifier zero-knowledge proof of knowledge system for proving that a vector of Pedersen commitments opens to a so-called "one-hot" vector (i.e., to a vector from...
On the Boomerang Uniformity of some Permutation Polynomials
Vectorial Boolean functions Boomerang uniformity Boomerang connectivity table
2019/8/2
The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials,...
On the alpha value of polynomials in the tower number field sieve algorithm
number field sieve discrete logarithm pairing-friendly curve
2019/8/2
In this paper, we provide a notable step towards filling the gap between theory (estimates of running-time) and practice (a discrete logarithm record computation) for the Tower Number Field Sieve (TNF...
On cryptographic parameters of permutation polynomials of the form xrh(x(q−1)/d)
Permutation Polynomials Differential Uniformity Boomerang Uniformity
2019/7/8
The differential uniformity, the boomerang uniformity, and the extended Walsh spectrum etc are important parameters to evaluate the security of S(substitution)-box. In this paper, we introduce efficie...
New Results about the Boomerang Uniformity of Permutation Polynomials
Finite Field Boomerang Connectivity Table Boomerang Uniformity
2019/1/29
In EUROCRYPT 2018, Cid et al. introduced a new concept on the cryptographic property of S-boxes: Boomerang Connectivity Table (BCT for short) for evaluating the subtleties of boomerang-style attacks. ...
Improved upper bound on root number of linearized polynomials and its application to nonlinearity estimation of Boolean functions
Boolean Functions Nonlinearity Linearized Polynomial Root Number
2018/12/3
To determine the dimension of null space of any given linearized polynomial is one of vital problems in finite field theory, with concern to design of modern symmetric cryptosystems. But, the known ge...
Homomorphic Secret Sharing for Low Degree Polynomials
secret sharing Homomorphic secret sharing
2018/11/12
Homomorphic secret sharing (HSS) allows nn clients to secret-share data to mm servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced compu...
How to leverage hardness of constant-degree expanding polynomials over $\mathbb{R}$ to build iO
FE Indistinguishability Obfuscation
2018/11/6
DD -restricted FE allows for useful evaluation of constant-degree polynomials, while only requiring the SXDH assumption over bilinear groups. As such, it is a powerful tool for leveraging hardness tha...
Decentralized Evaluation of Quadratic Polynomials on Encrypted Data
Decentralization FHE 2-DNF
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...
Efficient Evaluation of Low Degree Multivariate Polynomials in Ring-LWE Homomorphic Encryption Schemes
homomorphic encryption efficient polynomial evaluation ring lwe
2018/6/27
Homomorphic encryption schemes allow to perform computations over encrypted data. In schemes based on RLWE assumption the plaintext data is a ring polynomial. In many use cases of homomorphic encrypti...
4-bit crypto S-boxes: Generation with irreducible polynomials over Galois field GF(24) and cryptanalysis
public-key cryptography EPs
2018/6/13
4-bit crypto S-boxes play a significant role in encryption and decryption of many cipher algorithms from last 4 decades. Generation and cryptanalysis of generated 4-bit crypto S-boxes is one of the ma...
Homomorphic Rank Sort Using Surrogate Polynomials
Private computation encrypted computing fully homomorphic encryption
2018/3/26
In this paper we propose a rank based algorithm for sorting encrypted data using monomials. Greedy Sort is a sorting technique that achieves to minimize the depth of the homomorphic evaluations. It is...
Efficient Batch Zero-Knowledge Arguments for Low Degree Polynomials
Sigma-protocol zero-knowledge argument batch-verification
2018/1/11
The work of Bootle et al. (EUROCRYPT 2016) constructs an extremely efficient zero-knowledge argument for arithmetic circuit satisfiability in the discrete logarithm setting. However, the argument does...
On the exponents of APN power functions and Sidon sets, sum-free sets, and Dickson polynomials
sum-free sets Dickson polynomials
2017/12/11
On the exponents of APN power functions and Sidon sets, sum-free sets, and Dickson polynomials.