Add to ORKGWe present an oracle factorisation algorithm which finds a nontrivial factor of almost all squarefree positive integers $n$ based on the knowledge of the number of points on certain elliptic curves in residue rings modulo $n$
The polynomial time algorithm of Lenstra, Lenstra, and Lovász [15] for factoring integer polynomials...
We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the p...
Abstract. We address the problem of polynomial time factoring RSA moduli N1 = p1q1 with the help of ...
The problem of factoring integers in polynomial time with the help of an (infinitely powerful) oracl...
For a composite integer $N$ that we would like to factor, we consider a condition for the elliptic c...
AbstractLet n be a positive integer, and suppose n = Π piai is its prime factorization. Let θ(n) = Π...
Suppose that we want to factorize an integer N. We can use Lenstra's method, which is based on ellip...
International audienceWe revisit the problem of integer factorization with number-theoretic oracles,...
AbstractWe exhibit a deterministic algorithm for factoring polynomials in one variable over finite f...
AbstractThis paper gives an algorithm to factor a polynomialf(in one variable) over rings like Z/rZ ...
The goal of this paper is to describe the Elliptic Curve Method(ECM), an integer factorization algor...
Integer factoring is a curious number theory problem with wide applications in complexity and crypto...
We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and conside...
International audienceIn this paper we prove some divisibility properties of the cardinality of elli...
N.Garc\'ia-Fritz and H.Pasten showed that Hilbert's 10th problem is unsolvable in the ring of intege...
The polynomial time algorithm of Lenstra, Lenstra, and Lovász [15] for factoring integer polynomials...
We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the p...
Abstract. We address the problem of polynomial time factoring RSA moduli N1 = p1q1 with the help of ...
The problem of factoring integers in polynomial time with the help of an (infinitely powerful) oracl...
For a composite integer $N$ that we would like to factor, we consider a condition for the elliptic c...
AbstractLet n be a positive integer, and suppose n = Π piai is its prime factorization. Let θ(n) = Π...
Suppose that we want to factorize an integer N. We can use Lenstra's method, which is based on ellip...
International audienceWe revisit the problem of integer factorization with number-theoretic oracles,...
AbstractWe exhibit a deterministic algorithm for factoring polynomials in one variable over finite f...
AbstractThis paper gives an algorithm to factor a polynomialf(in one variable) over rings like Z/rZ ...
The goal of this paper is to describe the Elliptic Curve Method(ECM), an integer factorization algor...
Integer factoring is a curious number theory problem with wide applications in complexity and crypto...
We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and conside...
International audienceIn this paper we prove some divisibility properties of the cardinality of elli...
N.Garc\'ia-Fritz and H.Pasten showed that Hilbert's 10th problem is unsolvable in the ring of intege...
The polynomial time algorithm of Lenstra, Lenstra, and Lovász [15] for factoring integer polynomials...
We present two algorithms that, given a prime ell and an elliptic curve E/Fq, directly compute the p...
Abstract. We address the problem of polynomial time factoring RSA moduli N1 = p1q1 with the help of ...