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Improved Results on Factoring General RSA Moduli with Known Bits
Factorization General RSA moduli Known bits Integer method
2018/6/25
We revisit the factoring with known bits problem on general RSA moduli in the forms of N=prqsN=prqs for r,s≥1r,s≥1, where two primes pp and qq are of the same bit-size. The relevant moduli are inclusi...
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption
families of computational groups weak pseudo-freeness abelian groups
2017/11/28
A Certain Family of Subgroups of Zn⋆ Is Weakly Pseudo-Free under the General Integer Factoring Intractability Assumption.
This article appeared as Chapter 5 of the book "Topics in Computational Number Theory inspired by Peter L. Montgomery", edited by Joppe W. Bos and Arjen K. Lenstra and published by Cambridge Universit...
In this paper, we present a factoring algorithm that, assuming standard heuristics, uses just (logN)2/3+o(1)(logN)2/3+o(1) qubits to factor an integer NN in time Lq+o(1)Lq+o(1) where L=exp((logN)1/3(l...
Shor's Algorithm and Factoring: Don't Throw Away the Odd Orders
Shor's algorithm factoring
2017/2/20
Shor's algorithm factors an integer NN in two steps. The quantum step computes the order of amodNamodN where aa is relatively prime to NN. The classical step uses this order to factor NN. Descriptions...
Adversary-dependent Lossy Trapdoor Function from Hardness of Factoring Semi-smooth RSA Subgroup Moduli
factoring assumption semi-smooth RSA subgroup modulus lossy trapdoor function
2016/6/6
Lossy trapdoor functions (LTDFs), proposed by Peikert and Waters (STOC'08), are known to have a number of applications in cryptography. They have been constructed based on various assumptions, which i...
On Shor's Factoring Algorithm with More Registers and the Problem to Certify Quantum Computers
Shor’s factoring algorithm quantum register entanglement
2016/1/7
Shor’s factoring algorithm uses two quantum registers. By introducing
more registers we show that the measured numbers in these registers which are of the
same pre-measurement state, should be equal...
Use of SIMD-Based Data Parallelism to Speed up Sieving in Integer-Factoring Algorithms
Integer Factorization Sieving Multiple-Polynomial Quadratic Sieve Method
2016/1/4
Many cryptographic protocols derive their security from the apparent
computational intractability of the integer factorization problem. Currently,
the best known integer-factoring algorithms run in ...
Boneh et al. showed at Crypto 99 that moduli of the form N=p^r q can be factored in polynomial time when r=log p. Their algorithm is based on Coppersmith's technique for finding small roots of polynom...
In this paper, we study the problem of factoring an RSA
modulus N = pq in polynomial time, when p is a weak prime, that is, p
can be expressed as ap = u0 + M1u1 + . . . + Mkuk for some k integers
M...
Factoring as a Service
RSA factoring cloud computing
2015/12/22
The difficulty of integer factorization is fundamental to modern
cryptographic security using RSA encryption and signatures. Although a
512-bit RSA modulus was first factored in 1999, 512-bit RSA re...
A New Factoring Attack on Multi-Prime RSA with Small Prime Difference
Factoring attack multi-prime RSA small prime difference
2015/12/21
In this paper, we study the security of multi-prime RSA whose modulus is N = p1p2 · · · pr
for r ≥ 3 with small prime difference of size N
γ
. In ACISP 2013, Zhang and Takagi showed a
Fermat-like ...
Factoring RSA keys from certified smart cards: Coppersmith in the wild
factorization Coppersmith
2014/3/7
An attacker can efficiently factor at least 184 distinct 1024-bit RSA keys from Taiwan's national "Citizen Digital Certificate" database. The big story here is that these keys were generated by govern...
Cayley hash functions are a particular kind of cryptographic hash functions with very appealing properties. Unfortunately, their security is related to a mathematical problem whose hardness is not ver...
Cayley hash functions are a particular kind of cryptographic hash functions with very appealing properties. Unfortunately, their security is related to a mathematical problem whose hardness is not ver...