NDLI: How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves

Content Provider	Springer Nature Link
Author	Joye, Marc Quisquater, Jean Jacques Takagi, Tsuyoshi
Copyright Year	2001
Abstract	Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curve-based analogues, the length of the RSA-modulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSA-type cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSA-type systems over elliptic curves if a fixed point is found.
Starting Page	297
Ending Page	316
Page Count	20
File Format	PDF
ISSN	09251022
Journal	Designs, Codes and Cryptography
Volume Number	23
Issue Number	3
e-ISSN	15737586
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2001-01-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Data Structures, Cryptology and Information Theory Information and Communication, Circuits Combinatorics Convex and Discrete Geometry Electronic and Computer Engineering
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics Theoretical Computer Science Computer Science Applications

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