Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to Cryptanalysis

This dissertation contains algorithms for solving linear and polynomial systems of equations over GF(2). The objective is to provide fast and exact tools for algebraic cryptanalysis and other applications. Accordingly, it is divided into two parts. The first part deals with polynomial systems. Chapter 2 contains a successful cryptanalysis of Keeloq, the block cipher used in nearly all luxury automobiles. The attack is more than 16,000 times faster than brute force, but queries 0.62 × 2^32 plaintexts. The polynomial systems of equations arising from that cryptanalysis were solved via SAT-solvers. Therefore, Chapter 3 introduces a new method of solving polynomial systems of equations by converting them into CNF-SAT problems and using a SAT-solver. Finally, Chapter 4 contains a discussion on how SAT-solvers work internally. The second part deals with linear systems over GF(2), and other small fields (and rings). These occur in cryptanalysis when using the XL algorithm, which converts polynomial systems into larger linear systems. We introduce a new complexity model and data structures for GF(2)-matrix operations. This is discussed in Appendix B but applies to all of Part II. Chapter 5 contains an analysis of "the Method of Four Russians" for multiplication and a variant for matrix inversion, which is log n faster than Gaussian Elimination, and can be combined with Strassen-like algorithms. Chapter 6 contains an algorithm for accelerating matrix multiplication over small finite fields. It is feasible but the memory cost is so high that it is mostly of theoretical interest. Appendix A contains some discussion of GF(2)-linear algebra and how it differs from linear algebra in R and C. Appendix C discusses algorithms faster than Strassen's algorithm, and contains proofs that matrix multiplication, matrix squaring, triangular matrix inversion, LUP-factorization, general matrix in- version and the taking of determinants, are equicomplex. These proofs are already known, but are here gathered into one place in the same notation

Lucky thirteen: Breaking the TLS and DTLS record protocols

The Transport Layer Security (TLS) protocol aims to provide confidentiality and integrity of data in transit across untrusted networks. TLS has become the de facto secure protocol of choice for Internet and mobile applications. DTLS is a variant of TLS that is growing in importance. In this paper, we present distinguishing and plaintext recovery attacks against TLS and DTLS. The attacks are based on a delicate timing analysis of decryption processing in the two protocols. We include experimental results demonstrating the feasibility of the attacks in realistic network environments for several different implementations of TLS and DTLS, including the leading OpenSSL implementations. We provide countermeasures for the attacks. Finally, we discuss the wider implications of our attacks for the cryptographic design used by TLS and DTLS

Cryptanalysis of GlobalPlatform Secure Channel Protocols

GlobalPlatform (GP) card specifications are the de facto standards for the industry of smart cards. Being highly sensitive, GP specifications were defined regarding stringent security requirements. In this paper, we analyze the cryptographic core of these requirements; i.e. the family of Secure Channel Protocols (SCP). Our main results are twofold. First, we demonstrate a theoretical attack against SCP02, which is the most popular protocol in the SCP family. We discuss the scope of our attack by presenting an actual scenario in which a malicious entity can exploit it in order to recover encrypted messages. Second, we investigate the security of SCP03 that was introduced as an amendment in 2009. We find that it provably satisfies strong notions of security. Of particular interest, we prove that SCP03 withstands algorithm substitution attacks (ASAs) defined by Bellare et al. that may lead to secret mass surveillance. Our findings highlight the great value of the paradigm of provable security for standards and certification, since unlike extensive evaluation, it formally guarantees the absence of security flaws