Practical non-perfect fuzzy rainbow trade-off: reference design for fast FPGA and SSD implementation

Abstract

Time/memory trade-offs are general techniques used in the cryptanalysis of hash functions, block ciphers and stream ciphers that aim to reduce the computational effort at the cost of memory usage. Among these techniques the most modern algorithm is the Fuzzy-Rainbow trade-off, which has been used to attack the GSM A5/1 cipher in 2010. Most of the existing analyses of trade-off algorithms only take into consideration the main-memory model, which doesn't reflect the hierarchical (external) storage model of real world systems. Moreover, to the best of our knowledge, there are no publicly available implementations or designs that can show the performance level that can be obtained with modern off-the-shelf hardware. In this thesis we propose a reference hardware and software design for the cryptanalysis of stream ciphers and one-way functions based on FPGAs, SSDs and the Fuzzy Rainbow trade-off algorithm. The performances of the implementations of this design can be estimated through an analytical method based on the work by Hong and Moon. We evaluate our design by building a real world system that retrieves the key from plaintext/ciphertext pairs generated by a legacy 56-bits stream cipher. We experimentally confirm that the performance figures of our real world implementation lie in the expected ranges and we propose these figures as a reference of the performance level that can be achieved with off-the-shelf components in 2020.