搜索结果: 1-15 共查到“军事学 C/C Composite”相关记录25条 . 查询时间(0.073 秒)
We prove our result by reducing ff to (a variant of) the SINK-OF-VERIFIABLE-LINE problem, which is known to imply PPAD (and in fact CLS) hardness. The main building block of our reduction is a recentl...
On the Distribution of Quadratic Residues and Non-residues Modulo Composite Integers and Applications to Cryptography
Jacobi symbol probability distribution statistical distance
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...
Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
Optimal ate pairing twists of elliptic curves jacobian coordinates
2019/5/27
In this paper we present a comprehensive comparison between pairing-friendly elliptic curves, considering different curve forms and twists where possible. We define a measure of the efficiency of a pa...
Faster Initial Splitting for Small Characteristic Composite Extension Degree Fields
Discrete Log Finite fields Function Field Sieve Cryptography
2019/3/21
Let pp be a small prime and n=n1n2>1n=n1n2>1 be a composite integer. For the function field sieve algorithm applied to FpnFpn, Guillevic (2019) had proposed an algorithm for initial splitting of the t...
Non-Interactive Zero-Knowledge Proofs for Composite Statements
Non-interactive zero-knowledge sigma protocols SNARK
2018/6/5
The two most common ways to design non-interactive zero-knowledge (NIZK) proofs are based on Sigma protocols and QAP-based SNARKs. The former is highly efficient for proving algebraic statements while...
Condition on composite numbers easily factored with elliptic curve method
factoring number theory RSA
2017/5/12
For a composite integer NN that we would like to factor, we consider a condition for the elliptic curve method using NN as a scalar value to succeed and show that if NN has a prime factor pp such that...
Extended Tower Number Field Sieve with Application to Finite Fields of Arbitrary Composite Extension Degree
Discrete Logarithm Problem Number Field Sieve Finite Fields
2016/5/30
In a recent work, Kim and Barbulescu~(CRYPTO~2016) proposed an algorithm, called exTNFS, that improves asymptotic complexity for the discrete logarithm problems over Fpn in medium prime case, when the...
Improved Fully Homomorphic Encryption with Composite Number Modulus
fully homomorphic encryption multivariate algebraic equation Gr鯾ner basis
2016/1/27
Gentry抯 bootstrapping technique is the most famous method
of obtaining fully homomorphic encryption. In previous work I proposed
a fully homomorphic encryption without bootstrapping which has the
w...
Weak instances of composite order protocols.
Polynomial Spaces: A New Framework for Composite-to-Prime-Order Transformations
bilinear maps composite-order groups Groth-Sahai proofs
2016/1/9
At Eurocrypt 2010, Freeman presented a framework to convert cryptosystems based on compositeorder
groups into ones that use prime-order groups. Such a transformation is interesting not only from
a c...
Obfuscating Circuits via Composite-Order Graded Encoding
Obfuscation Graded Encoding Schemes
2016/1/5
We present a candidate obfuscator based on composite-order Graded Encoding Schemes
(GES), which are a generalization of multilinear maps. Our obfuscator operates on circuits
directly without convert...
Fully Homomorphic Encryption with Composite Number Modulus
fully homomorphic encryption multivariate algebraic equation Gr鯾ner basis
2015/12/22
Gentry抯 bootstrapping technique is the most famous method
of obtaining fully homomorphic encryption. In previous work I proposed a
fully homomorphic encryption without bootstrapping which has the we...
A Note on Bilinear Groups of a Large Composite Order
bilinear groups of composite order homomorphic public-key encryption
2014/3/5
We remark that the structure of bilinear groups of a large composite order(at least 1024 bits) could make group operation inefficient and lose the advantages of elliptic curve cryptography which gaine...
New Trapdoor Projection Maps for Composite-Order Bilinear Groups
foundations bilinear groups
2014/3/7
An asymmetric pairing over groups of composite order is a bilinear map $e: G_1 \times G_2 \to G_T$ for groups $G_1$ and $G_2$ of composite order $N=pq$. We observe that a recent construction of pairin...
A Profitable Sub-Prime Loan: Obtaining the Advantages of Composite Order in Prime-Order Bilinear Groups
bilinear groups prime-order groups
2014/3/12
Composite-order bilinear groups provide many structural features that have proved useful for both constructing cryptographic primitives and as a technique in security reductions. Despite these conveni...