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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...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...
Scrutinizing the Tower Field Implementation of the $\mathbb{F}_{2^8}$ Inverter -- with Applications to AES, Camellia, and SM4
Tower field Inverter S-box
2019/6/24
The tower field implementation of the F28F28 inverter is not only the key technique for compact implementations of the S-boxes of several internationally standardized block ciphers such as AES, Camell...
Field Extension in Secret-Shared Form and Its Applications to Efficient Secure Computation
secure computation secret sharing, active security
2019/4/16
Secure computation enables participating parties to jointly compute a function over their inputs while keeping them private. Secret sharing plays an important role for maintaining privacy during the c...
More Efficient Algorithms for the NTRU Key Generation using the Field Norm
lattice techniques public-key cryptography quantum cryptography
2019/1/9
NTRU lattices are a class of polynomial rings which allow for compact and efficient representations of the lattice basis, thereby offering very good performance characteristics for the asymmetric algo...
Higher dimensional sieving for the number field sieve algorithms
public-key cryptography exTNFS
2018/11/6
Since 2016 and the introduction of the exTNFS (extended Tower Number Field Sieve) algorithm, the security of cryptosystems based on non- prime finite fields, mainly the paring and torus-based one, is ...
A signature scheme from the finite field isomorphism problem
Digital signatures finite field isomorphism problem lattice-based signature
2018/7/16
In a recent paper the authors and their collaborators proposed a new hard problem, called the finite field isomorphism problem, and they used it to construct a fully homomorphic encryption scheme. In ...
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...
Decomposition of Permutations in a Finite Field
Carlitz Theorem decomposition of power functions threshold implementations
2018/1/30
We describe a method to decompose any power permutation, as a sequence of power permutations of lower algebraic degree. As a result we obtain decompositions of the inversion in GF(2n)GF(2n) for small ...
Parameterization of Edwards curves on the rational field Q with given torsion subgroups
Edwards curve twisted Edwards curve torsion subgroups
2018/1/29
This paper presents the basic concepts of the Edwards curves, twisted Edwards curves and the point addition laws on these curves. The main result is the parameterization of the Edward curve with the g...
Efficient provable-secure NTRUEncrypt over any cyclotomic field
NTRU Ideal lattice Canonical embedding
2017/11/20
NTRUEncrypt is a fast lattice-based cryptosystem and a probable alternative of the existing public key schemes. The existing provable-secure NTRUEncrypts are limited by the cyclotomic field it works o...
Field lifting for smaller UOV public keys
Post-Quantum Cryptography Multivariate Cryptography Signature Schemes
2017/8/17
Most Multivariate Quadratic (MQ) signature schemes have a very large public key, which makes them unsuitable for many applications, despite attractive features such as speed and small signature sizes....
On the discrete logarithm problem for prime-field elliptic curves
elliptic curve discrete logarithm problem prime field
2017/6/27
In recent years several papers have appeared investigating the classical discrete logarithm problem for elliptic curves by means of the multivariate polynomial approach based on the celebrated summati...
(Finite) Field Work: Choosing the Best Encoding of Numbers for FHE Computation
Fully Homomorphic Encryption FHE Encoding
2017/6/22
Fully Homomorphic Encryption (FHE) schemes are a powerful tool that allows arbitrary computations on encrypted data. This makes them a promising tool for a variety of use cases that require outsourcin...
Fully Homomorphic Encryption from the Finite Field Isomorphism Problem
Finite field isomorphism fully homomorphic encryption lattice-based cyrptopgraphy
2017/6/9
If qq is a prime and nn is a positive integer then any two finite fields of order qnqn are isomorphic. Elements of these fields can be thought of as polynomials with coefficients chosen modulo qq, and...