Notions for RSA integers Online publication date: Wed, 11-Jun-2014
by Daniel Loebenberger; Michael Nüsken
International Journal of Applied Cryptography (IJACT), Vol. 3, No. 2, 2014
Abstract: The key-generation algorithm for the RSA cryptosystem is specified in several standards, such as PKCS#1, IEEE 1363-2000, FIPS 186-3, ANSI X9.44, or ISO/IEC 18033-2. All of them substantially differ in their requirements. This indicates that for computing a 'secure' RSA modulus it does not matter how exactly one generates RSA integers. In this work, we show that this is indeed the case to a large extent. First, we give a theoretical framework that enables us to easily compute the entropy of the output distribution of the considered standards and show that it is comparatively high. To do so, we compute for each standard the number of integers they define (up to an error of very small order) and discuss different methods of generating integers of a specific form. Second, we show that factoring such integers is hard, provided factoring a product of two primes of similar size is hard.
Online publication date: Wed, 11-Jun-2014
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Applied Cryptography (IJACT):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.If you still need assistance, please email firstname.lastname@example.org