J. Cryptology (2001) 14: 255–293 DOI: 10.1007/s00145-001-0009-4 © 2001 International Association for Cryptologic Research Selecting Cryptographic Key Sizes Arjen K. Lenstra Citibank, N.A., 1 North Gate Road, Mendham, NJ 07945-3104, U.S.A.
[email protected] and Technische Universiteit Eindhoven Eric R. Verheul PricewaterhouseCoopers, GRMS Crypto Group, Goudsbloemstraat 14, 5644 KE Eindhoven, The Netherlands eric.verheul@[nl.pwcglobal.com, pobox.com] Communicated by Andrew Odlyzko Received September 1999 and revised February 2001 Online publication 14 August 2001 Abstract. In this article we offer guidelines for the determination of key sizes for symmetric cryptosystems, RSA, and discrete logarithm-based cryptosystems both over finite fields and over groups of elliptic curves over prime fields. Our recommendations are based on a set of explicitly formulated parameter settings, combined with existing data points about the cryptosystems. Key words. Symmetric key length, Public key length, RSA, ElGamal, Elliptic curve cryptography, Moore’s law. 1. Introduction 1.1. The Purpose of This Paper Cryptography is one of the most important tools that enable e-commerce because cryp- tography makes it possible to protect electronic information. The effectiveness of this protection depends on a variety of mostly unrelated issues such as cryptographic key size, protocol design, and password selection. Each of these issues is equally important: if a key is too small, or if a protocol is badly designed or incorrectly used, or if a pass- word is poorly selected or protected, then the protection fails and improper access can be gained. In this article we give some guidelines for the determination of cryptographic key sizes.