Adleman-Manders-Miller Root Extraction Method Revisited

نویسندگان

  • Zhengjun Cao
  • Qian Sha
  • Xiao Fan
چکیده

In 1977, Adleman, Manders and Miller had briefly described how to extend their square root extraction method to the general rth root extraction over finite fields, but not shown enough details. Actually, there is a dramatic difference between the square root extraction and the general rth root extraction because one has to solve discrete logarithms for rth root extraction. In this paper, we clarify their method and analyze its complexity. Our heuristic presentation is helpful to grasp the method entirely and deeply.

برای دانلود رایگان 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

Remarks on the Pocklington and Padró-Sáez Cube Root Algorithm in 𝔽q

We clarify and generalize a cube root algorithm in Fq proposed by Pocklington [1], and later rediscovered by Padró and Sáez [2]. We correct some mistakes in [2] and give a full generalization of the result in [1, 2] for the cube root algorithm. We also give the comparison of the implementation of Pocklington and Padró-Sáez algorithm with two most popular cube root algorithms, namely the Adleman...

متن کامل

A remark on the computation of cube roots in finite fields

We consider the computation of cube roots in finite fields. For the computation of square roots in finite fields, there are two typical methods; the Tonelli-Shanks method [9, 12] and the Cipolla-Lehmer method [4, 6]. The former can be extended easily to the case of r-th roots, which is called the Adleman-Manders-Miller method [1], but it seems to be difficult to extend the latter to more genera...

متن کامل

New Cube Root Algorithm Based on Third Order Linear Recurrence Relation in Finite Field

We present a new cube root algorithm in finite field Fq with q a power of prime, which extends Cipolla-Lehmer type algorithms and has lower complexity than Tonelli-Shanks type algorithms. Efficient computation of r-th root in Fq has many applications in computational number theory and many other related areas. There are two standard algorithms for computing rth root in finite field. One is Adle...

متن کامل

Supercritical fluid extract of Lycium chinense Miller root inhibition of melanin production and its potential mechanisms of action

BACKGROUND The mode of action of Lycium chinense Miller root extract in skin care has never been explored. In the present study, Lycium chinense Miller root was extracted by the supercritical fluid CO2 extraction method. METHODS In the present study, the components of the root extract were analyzed by HPLC. The effects of the extract on tyrosinase activity and melanin content were determined ...

متن کامل

Some New Tables of the Largest Root of a Matrix in Multivariate Analysis: a Computer Approach from 2 to 6

The distribution of the non-null characteristic roots of a matrix derived from sample observations taken from multivariate normal populations is of fundamental of importance in multivariate analysis. The Fisher-Girshick-Shu-Roy distribution (1939), which has interested statisticians for more than 6 decades, is revisited. Instead of using K.C.S. Pillai’s method by neglecting higher order terms o...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2011