搜索结果: 1-15 共查到“Mersenne”相关记录17条 . 查询时间(0.064 秒)
Quantum LLL with an Application to Mersenne Number Cryptosystems
quantum attack lattice reduction Grover's algorithm
2019/9/16
In this work we analyze the impact of translating the well-known LLL algorithm for lattice reduction into the quantum setting. We present the first (to the best of our knowledge) quantum circuit repre...
Improved Cryptanalysis of the AJPS Mersenne Based Cryptosystem
public-key cryptography Mersenne numbers LLL
2019/6/3
At Crypto 2018, Aggarwal, Joux, Prakash and Santha (AJPS) described a new public-key encryption scheme based on Mersenne numbers. Shortly after the publication of the cryptosystem, Beunardeau et al. d...
The Mersenne Low Hamming Combination Search Problem can be reduced to an ILP Problem
Post-Quantum Cryptography Cryptanalysis Public-Key Cryptography Integer Linear Programming
2019/5/13
In 2017, Aggarwal, Joux, Prakash, and Santha proposed an innovative NTRU-like public-key cryptosystem that was believed to be quantum resistant, based on Mersenne prime numbers q=2N−1q=2N−...
Post-Quantum Provably-Secure Authentication and MAC from Mersenne Primes
secret-key cryptography MERS
2019/4/23
This paper presents a novel, yet efficient secret-key authentication and MAC, which provide post-quantum security promise, whose security is reduced to the quantum-safe conjectured hardness of Mersenn...
Efficient Inversion In (Pseudo-)Mersenne Prime Order Fields
finite fields inversion multiplication
2018/11/5
Efficient scalar multiplication algorithms require a single finite field inversion at the end to convert from projective to affine coordinates. This inversion consumes a significant proportion of the ...
On inversion modulo pseudo-Mersenne primes
Elliptic Curves side-channel secure modular inversion
2018/11/2
It is well established that the method of choice for implementing a side-channel secure modular inversion, is to use Fermat's little theorem. So 1/x=xp−2modp1/x=xp−2modp. This can be calcu...
Aggarwal, Joux, Prakash and Santha recently introduced a new potentially quantum-safe public-key cryptosystem, and suggested that a brute-force attack is essentially optimal against it. They consider ...
In a recent paper, Aggarwal, Joux, Prakash, and Santha (AJPS) describe an ingenious public-key cryptosystem mimicking NTRU over the integers. This algorithm relies on the properties of Mersenne primes...
A New Public-Key Cryptosystem via Mersenne Numbers
public-key cryptosystem Public-Key Cryptosystem via Mersenne Numbers
2017/5/31
In this work, we propose a new public-key cryptosystem whose security is based on the computational intractability of the following problem: Given a Mersenne number p = 2^n - 1, where n is a prime, a ...
Mersenne factorization factory
Mersenne numbers factorization factory special number field sieve
2016/1/7
We present new factors of seventeen Mersenne numbers, obtained using a variant of
the special number field sieve where sieving on the algebraic side is shared among the numbers.
It reduced the overa...
FourQ: four-dimensional decompositions on a Q-curve over the Mersenne prime
four-dimensional decompositions Mersenne prime
2015/12/29
We introduce FourQ, a high-security, high-performance elliptic curve that targets the 128-
bit security level. At the highest arithmetic level, cryptographic scalar multiplications on FourQ can use
...
Overpseudoprimes, and Mersenne and Fermat numbers as primover numbers
Mersenne numbers cyclotomic cosets of 2 modulo n Poulet pseudoprime super-Poulet pseudoprime overpseudoprime
2012/6/19
We introduce a new class of pseudoprimes-so called "overpseudoprimes to base $b$", which is a subclass of strong pseudoprimes to base $b$. Denoting via $|b|_n$ the multiplicative order of $b$ modulo $...
Mersenne Primes in Real Quadratic Fields
Mersenne Primes Real Quadratic Fields Number Theory
2012/5/24
The concept of Mersenne primes is studied in real quadratic fields of class number 1. Computational results are given. The field $Q(\sqrt{2})$ is studied in detail with a focus on representing Mersenn...
Generalised Mersenne Numbers Revisited
implementation / elliptic curve cryptography high-speed arithmetic generalised Mersenne numbers cyclotomic primes generalised repunit primes
2012/3/26
Generalised Mersenne Numbers (GMNs) were defined by Solinas in 1999 and feature in the NIST Digital Signature Standard (FIPS 186-2) for use in elliptic curve cryptography. Their form is such that modu...
广义Mersenne数中的奇完全数
广义Mersenne数 奇完全数 下界
2012/11/22
设p是奇素数，a和b是适合a>b，gcd(a,b)=1的正整数.设f(a,b,p)=(ap-bp)/(a-b).运用初等数论方法证明了当log a≤max(7log p,(2p-1-1)log p)时，f(a,b,p)不是奇完全数.