General Principles of Algebraic Attacks and New Design Criteria for Cipher Components

  • Nicolas T. Courtois
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3373)

Abstract

This paper is about the design of multivariate public key schemes, as well as block and stream ciphers, in relation to recent attacks that exploit various types of multivariate algebraic relations. We survey these attacks focusing on their common fundamental principles and on how to avoid them. From this we derive new very general design criteria, applicable for very different cryptographic components. These amount to avoiding (if possible) the existence of, in some sense “too simple” algebraic relations. Though many ciphers that do not satisfy this new paradigm probably still remain secure, the design of ciphers will never be the same again.

Keywords

algebraic attacks polynomial relations multivariate equations finite fields design of cryptographic primitives generalised linear cryptanalysis multivariate public key encryption and signature schemes HFE Quartz Sflash stream ciphers Boolean functions combiners with memory block ciphers AES Rijndael Serpent elimination methods Gröbner bases 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nicolas T. Courtois
    • 1
  1. 1.Axalto Cryptographic Research & Advanced SecurityLouveciennes CedexFrance

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