Download Algorithmic Number Theory: 5th International Symposium, by Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.) PDF

By Manjul Bhargava (auth.), Claus Fieker, David R. Kohel (eds.)

From the reviews:

"The ebook includes 39 articles approximately computational algebraic quantity thought, mathematics geometry and cryptography. … The articles during this ebook mirror the wide curiosity of the organizing committee and the individuals. The emphasis lies at the mathematical conception in addition to on computational effects. we propose the e-book to scholars and researchers who are looking to examine present learn in quantity concept and mathematics geometry and its applications." (R. Carls, Nieuw Archief voor Wiskunde, Vol. 6 (3), 2005)

Show description

Read Online or Download Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 Proceedings PDF

Best international_1 books

Static Analysis: 15th International Symposium, SAS 2008, Valencia, Spain, July 16-18, 2008. Proceedings

This ebook constitutes the refereed lawsuits of the fifteenth foreign Symposium on Static research, SAS 2008, held in Valencia, Spain in July 2008 - co-located with LOPSTR 2008, the overseas Symposium on Logic-based application Synthesis and Transformation, PPDP 2008, the foreign ACM SIGPLAN Symposium on rules and perform of Declarative Programming, and PLID 2008, the overseas Workshop on Programming Language Interference and Dependence.

The International Biotechnology Directory 1993: Products, Companies, Research and Organizations

Presents the reader with info on greater than 8500 businesses, examine centres and educational associations concerned about new and confirmed applied sciences. This 1993 variation has greater than seven-hundred association listings combining advertisement and non-commercial enterprises.

Extra resources for Algorithmic Number Theory: 5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 Proceedings

Sample text

Given t ∈ K × , define the denominator ideal den(t) = { b ∈ OK : bt ∈ OK } and the numerator ideal num(t) = den(t−1 ). Also define num(0) to be the zero ideal. These ideals behave in the obvious way upon extension of the field. Lemma 3. 1. For fixed m, n ∈ Z≥0 , the set of (x1 , . . , xm , y1 , . . , yn ) in K m+n such that the fractional ideal (x1 , . . , xm ) divides the fractional ideal (y1 , . . , yn ) is diophantine over OK . 2. The set of (t, u) ∈ K × × K × such that den(t) | den(u) is diophantine over OK .

Miller in 1985 [29]. Indeed, since elliptic curves have a group structure, they nicely fit as a replacement for more traditional groups in discrete logarithm based systems such as Diffie–Hellman or ElGamal. Moreover, since there is no non-generic algorithm for computing discrete logarithms on elliptic curves, it is possible to reach a high security level while using relatively short keys. However, in [27] Menezes, Okamoto and Vanstone showed that some special elliptic curves, called supersingular curves, are weaker than general elliptic curves.

2. 3. 4. 5. P = P0 t0 = x(P0 ), t = x(P ), t = x(P ) (μ + 1)(μ + 2) . . (μ + n) | den(t0 ) den(t) | den(t ) den(t) | num((t/t − μ)2 ) It follows from Lemma 3 that S is diophantine over OK . Suppose m ∈ Z≥1 . We wish to show that μ := m2 belongs to S. By Lemma 10, there exists P0 ∈ rE(K) − {O} such that (μ + 1)(μ + 2) . . (μ + n) | den(x(P0 )). Let P = P0 and P = mP . Let t0 = x(P0 ), t = x(P ), and t = x(P ). Then conditions (1), (2), and (3) in the definition of S are satisfied, and (4) and (5) follow from Lemmas 9 and 11, respectively.

Download PDF sample

Rated 4.83 of 5 – based on 4 votes