搜索结果: 1-15 共查到“Finite field”相关记录22条 . 查询时间(0.093 秒)
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...
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 ...
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 ...
(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...
Quantum one-way permutation over the finite field of two elements
Quantum one-way permutation CHSH inequality Controlled NOT gate
2017/5/2
In quantum cryptography, a one-way permutation is a bounded unitary operator U:H↦HU:H↦H on a Hilbert space HH that is easy to compute on every input, but hard to invert given the image of ...
Efficient Finite field multiplication for isogeny based post quantum cryptography
public-key cryptography post quantum cryptography
2016/12/7
Isogeny based post-quantum cryptography is one of the most recent addition to the family of quantum resistant cryptosystems. In this paper, we propose an efficient modular multiplication algorithm for...
Bit Security of the CDH Problems over Finite Field
CDH Diffie-Hellman problem d-th CDH problem
2016/1/7
It is a long-standing open problem to prove the existence of (deterministic) hard-core predicates
for the Computational Diffie-Hellman (CDH) problem over finite fields, without resorting to
the gene...
Improved Side-Channel Analysis of Finite-Field Multiplication
Side-Channel Analysis Galois Field Multiplication LPN problem
2015/12/30
A side-channel analysis of multiplication in GF(2^{128}) has recently been published by Bela飀, Fouque and G閞ard at Asiacrypt 2014, with an application to AES-GCM. Using the least significant bit of th...
A fast integer-based batch full-homomorphic encryption scheme over finite field
full-homomorphic integer-based
2014/3/5
In view of the problems that the plaintext space is too small in the existing schemes. In this paper, a new improved scheme is presented by improving the DGHV scheme. The plaintext space of the improv...
Trace Expression of r-th Root over Finite Field
applications / finite field r-th root linear recurrence relation
2013/2/21
Efficient computation of $r$-th root in $\mathbb F_q$ has many applications in computational number theory and many other related areas. We present a new $r$-th root formula which generalizes M\"{u}ll...
New Cube Root Algorithm Based on Third Order Linear Recurrence Relation in Finite Field
applications / cube root algorithm Cipolla-Lehmer algorithm
2013/2/21
In this paper, we present a new cube root algorithm in finite field $\mathbb{F}_{q}$ with $q$ a power of prime, which extends the Cipolla-Lehmer type algorithms \cite{Cip,Leh}. Our cube root method is...
Cohomology of Kac-Moody groups over a finite field
Cohomology classifying spaces Kac-Moody groups
2012/6/26
We compute the mod $p$ cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from $p$.
Automorphisms of Drinfeld half-spaces over a finite field
Non-archimedean analytic geometry Berkovich spaces Drinfeld upper half-space birational transformations
2012/6/21
We show that the automorphism group of Drinfeld's half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the s...
A survey of the Poincaré Center Problem in degree 3 using finite field heuristics
survey Poincaré Center Problem degree 3
2011/2/21
We compare a heuristic count of components of the center variety in degree 3 with the equivalent count obtained from known families.From this comparison we conjecture that more than 100 unknown compon...