Analyzing standards for RSA integers

Daniel Loebenberger (cosec - b-it)

Thursday 9 June 2011, 15.00, b-it 1.25 (cosec meeting room)

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 talk we show that this is indeed the case to a large extend: First, we will 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.