Structure computation and discrete logarithms in finite abelian p-groups

نویسنده

  • Andrew V. Sutherland
چکیده

We present a generic algorithm for computing discrete logarithms in a finite abelian p-group H, improving the Pohlig–Hellman algorithm and its generalization to noncyclic groups by Teske. We then give a direct method to compute a basis for H without using a relation matrix. The problem of computing a basis for some or all of the Sylow p-subgroups of an arbitrary finite abelian group G is addressed, yielding a Monte Carlo algorithm to compute the structure of G using O(|G|1/2) group operations. These results also improve generic algorithms for extracting pth roots in G.

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Quantum factoring, discrete logarithms, and the hidden subgroup problem

Amongst the most remarkable successes of quantum computation are Shor’s efficient quantum algorithms for the computational tasks of integer factorisation and the evaluation of discrete logarithms. In this article we review the essential ingredients of these algorithms and draw out the unifying generalization of the so-called abelian hidden subgroup problem. This involves an unexpectedly harmoni...

متن کامل

Discrete Logarithms: Recent Progress

We summarize recent developments on the computation of discrete logarithms in general groups as well as in some specialized settings. More specifically , we consider the following abelian groups: the multiplicative group of nite elds, the group of points of an elliptic curve over a nite eld, and the class group of quadratic number elds.

متن کامل

THE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS

A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.  

متن کامل

Quantum computation of discrete logarithms in semigroups

We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor’s algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete logarithms in semigroups are insecure against quantum attacks. In contrast, we show that some generalizations of the discrete log problem are hard in semigroup...

متن کامل

Collision bounds for the additive Pollard rho algorithm for solving discrete logarithms

We prove collision bounds for the Pollard rho algorithm to solve the discrete logarithm problem in a general cyclic group G. Unlike the setting studied by Kim et al., we consider additive walks: the setting used in practice to solve the elliptic curve discrete logarithm problem. Our bounds differ from the birthday bound O. p jGj/ by a factor of p log jGj and are based on mixing time estimates f...

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

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

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Math. Comput.

دوره 80  شماره 

صفحات  -

تاریخ انتشار 2011