By Igor Shparlinski

The ebook introduces new methods of utilizing analytic quantity idea in cryptography and comparable parts, akin to complexity conception and pseudorandom quantity generation.

Key issues and features:

- quite a few reduce bounds at the complexity of a few quantity theoretic and cryptographic difficulties, linked to classical schemes similar to RSA, Diffie-Hellman, DSA in addition to with fairly new schemes like XTR and NTRU

- a sequence of very contemporary effects approximately convinced vital features (period, distribution, linear complexity) of a number of well-known pseudorandom quantity turbines, reminiscent of the RSA generator, Blum-Blum-Shub generator, Naor-Reingold generator, inversive generator, and others

- one of many valuable instruments is bounds of exponential sums, that are mixed with different quantity theoretic equipment corresponding to lattice aid and sieving

- a few open difficulties of alternative point of hassle and recommendations for additional research

- an in depth and updated bibliography

Cryptographers and quantity theorists will locate this e-book valuable. the previous can know about new quantity theoretic strategies that have proved to be worthwhile cryptographic instruments, the latter approximately new tough components of functions in their skills.

Show description

Read Online or Download Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness PDF

Similar security & encryption books

ExamWise For Exam 1D0-460 CIW Internetworking Professional by Chad Bayer PDF

A part of the ExamWise to CIW Certification sequence, this new Self support and Interactive examination learn relief is now on hand for candidate's getting ready to take a seat the CIW 1D0-460 Internetworking expert examination. The e-book covers the data linked to all of the examination themes intimately and comprises info present in no different ebook.

Mobile Access Safety: Beyond BYOD by Dominique Assing PDF

Over contemporary years, the volume of cellular gear that should be hooked up to company networks remotely (smartphones, laptops, and so forth. ) has elevated speedily. leading edge improvement views and new trends equivalent to BYOD (bring your individual machine) are exposing company info structures greater than ever to varied compromising threats.

Introduction to computer networks and cybersecurity - download pdf or read online

"Draft creation to computing device Networking and Cybersecurity To the scholar it's tricky to overstate the significance of machine networks and community safeguard in trendy global. they've got turn into such a vital part of our life that just a moment's mirrored image is needed to delineate the numerous ways that they effect basically each element of our lives.

New PDF release: Official (ISC)2® Guide to the CAP® CBK®, Second Edition

"Providing an summary of certification and accreditation, the second one variation of this formally sanctioned advisor demonstrates the practicality and effectiveness of C & A as a probability administration technique for IT platforms in private and non-private enterprises. It permits readers to record the prestige in their safeguard controls and how to safe IT structures through general, repeatable tactics.

Additional info for Cryptographic Applications of Analytic Number Theory: Complexity Lower Bounds and Pseudorandomness

Sample text

7, we obtain the desired estimate. 16 has been used in [526] to obtain new bounds of Gauss sums in finite fields. 3 of [407]. 10. For any E > 0 there exists "I > 0 such that for any non-trivial multiplicative character X modulo p IX~I X(X)I :::; Hp-' for H :::: pI/HE and sufficiently large p. Part 1: Preliminaries 42 It is known that the Extended Riemann Hypothesis implies non-trivial upper bounds for much shorter sums. In particular, we use a bound which follows from one of the results of [230].

For the second configuration we merely ignore the congruence condition on Xi4 and remark that it is uniquely defined for each choice of XiI' Xi 2, Xi3 for which we have at most (p - 1)3/d l d 2 possibilities. 123 .... 11) we obtain ~ I~ e 4 p (ag X + cgxy)1 :::; 14((5/3)p14/3 + O(p13/:l). lO) we derive the desired result. D In fact, a more general estimate has been obtained in [94] which applies to elements of A E IF p of multiplicative order T :2': p3/ He . 14) We fix an element 9 E IF; of multiplicative order t and consider double exponential sums Sa(X, Y) = LL e p (ag XY ) , xEXyEY where a E lFp and X,Y ~ 7l.

6 with t = 4, we see that for each quadruple (XI,X2,X3,X4), there are at most values of y = 1, ... ,p - 1 which satisfy that system, where d = min maxgcd(xi l:Si:S4 Hi xJ,p -1). 12) 52 Part I: Preliminaries We claim that the number of quadruples (Xl, X2. X;l. 12) and which satisfy the first congruence of the above system of congruences does not exceed p3d-2 + p2. 12) holds belongs to one of the following two types of configuration. In the first case they can be separated into two pairs {i l ,i 2 ,i 3 ,i4 } = {1,2,3,4} and such that There are three choices of a partner for Xl (XiI' Xi2) and (Xi3' Xi4) with and this determines the pairings.

Download PDF sample

Rated 4.04 of 5 – based on 38 votes