Factoring Integers with Elliptic Curves

نویسندگان

چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Factoring integers with elliptic curves

This paper is devoted to the description and analysis of a new algorithm to factor positive integers. It depends on the use of elliptic curves. The new method is obtained from Pollard's (p — l)-method (Proc. Cambridge Philos. Soc. 76 (1974), 521-528) by replacing the multiplicative group by the group of points on a random elliptic curve. It is conjectured that the algorithm determines a non-tri...

متن کامل

Factoring Integers Using Elliptic Curves over Q

For the integer D = pq of the product of two distinct odd primes, we construct an elliptic curve E2rD : y 2 = x3 − 2rDx over Q, where r is a parameter dependent on the classes of p and q modulo 8, and show, under Birch and Swinnerton-Dyer conjecture, that the elliptic curve has rank one and vp(x([k]Q)) 6= vq(x([k]Q)) for odd k and a generator Q of the free part of E2rD(Q). Thus we can get p or ...

متن کامل

Factoring integers and computing elliptic curve rational points

We conjecturally relate via a polynomial-time reduction, a subproblem of integer factoring to the problem of computing the MordellWeil group of an elliptic curve from a special family. This raises an interesting question about the growth of the height of the generators of the above group with respect to the discriminant of the elliptic curve. We gather numerical evidence to shed light on this b...

متن کامل

Fast Factoring of Integers

An algorithm is given to factor an integer with N digits in lnN steps, with m approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a further exponential speedup. Factorization of large integers is important to many areas of pure mathematics and has practical applications in applied math including c...

متن کامل

Factoring Polynomials for Constructing Pairing-friendly Elliptic Curves

In this paper we present a new method to construct a polynomial u(x) ∈ Z[x] which will make Φk(u(x)) reducible. We construct a finite separable extension of Q(ζk), denoted as E. By primitive element theorem, there exists a primitive element θ ∈ E such that E = Q(θ). We represent the primitive k-th root of unity ζk by θ and get a polynomial u(x) ∈ Q[x] from the representation. The resulting u(x)...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: The Annals of Mathematics

سال: 1987

ISSN: 0003-486X

DOI: 10.2307/1971363