LNCS 2729 Algebraic Attacks on Combiners with Memory 1ST EDITION BY Frederik Armknecht, Matthias Krause ISBN 9783540406747

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ISBN 10:
ISBN 13: 9783540406747
Author: Frederik Armknecht, Matthias Krause

Recently, algebraic attacks were proposed to attack several cryptosystems, e.g. AES, LILI-128 and Toyocrypt. This paper extends the use of algebraic attacks to combiners with memory. A (k,l)-combiner consists of k parallel linear feedback shift registers (LFSRs), and the nonlinear filtering is done via a finite automaton with k input bits and l memory bits. It is shown that for (k,l)-combiners, nontrivial canceling relations of degree at most ⌈k(l+1)/2⌉ exist. This makes algebraic attacks possible. Also, a general method is presented to check for such relations with an even lower degree. This allows to show the invulnerability of certain (k,l)-combiners against this kind of algebraic attacks. On the other hand, this can also be used as a tool to find improved algebraic attacks.

Inspired by this method, the E ₀ keystream generator from the Bluetooth standard is analyzed. As it turns out, a secret key can be recovered by solving a system of linear equations with 2^23.07 unknowns. To our knowledge, this is the best published attack on the E ₀ keystream generator yet.

LNCS 2729 Algebraic Attacks on Combiners with Memory 1ST EDITION Table of contents : 

1. Introduction

   • 1.1 Overview of Cryptographic Attacks
   • 1.2 The Importance of Combiners in Cryptography
   • 1.3 Memory and State in Cryptographic Systems
   • 1.4 Scope of the Book

2. Preliminaries

   • 2.1 Algebraic Cryptanalysis: Basics
   • 2.2 Combiners and Their Role in Cryptographic Systems
   • 2.3 Memory 1 Models in Cryptographic Functions
   • 2.4 Algebraic Structures in Cryptographic Attacks

3. Combiners with Memory: A Formal Model

   • 3.1 Definition and Characteristics of Combiners
   • 3.2 Memory-1 Models and their Impact on Cryptanalysis
   • 3.3 Mathematical Foundations for Analyzing Combiners

4. Algebraic Attacks on Combiners

   • 4.1 Concept of Algebraic Attacks
   • 4.2 Attacking Linear and Nonlinear Combiners
   • 4.3 Key Recovery Using Algebraic Techniques
   • 4.4 Techniques for Solving Algebraic Systems

5. Case Studies

   • 5.1 Case Study 1: Cryptosystem with Linear Combiners
   • 5.2 Case Study 2: Cryptosystem with Nonlinear Combiners
   • 5.3 Case Study 3: Memory-1 Combiner Attacks

6. Advanced Algebraic Techniques

   • 6.1 Gröbner Basis Methods in Algebraic Cryptanalysis
   • 6.2 Use of Polynomial Equations in Cryptanalysis
   • 6.3 Solving Overdetermined Systems
   • 6.4 Improvements in Algebraic Attacks on Combiners

7. Mitigation Techniques

   • 7.1 Reducing Vulnerabilities in Memory-1 Combiners
   • 7.2 Enhancing the Security of Cryptographic Functions
   • 7.3 Recommendations for Designing Resilient Cryptosystems

8. Conclusion

   • 8.1 Summary of Findings
   • 8.2 Open Problems in Algebraic Cryptanalysis
   • 8.3 Future Directions in Cryptographic Research

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