Paper 2009/020

Applying Time-Memory-Data Trade-Off to Meet-in-the-Middle Attack

Jiali Choy and Khoongming Khoo and Chuan-Wen Loe

Abstract

In this paper, we present several new attacks on multiple encryption block ciphers based on the meet-in-the-middle attack. In the first attack (GDD-MTM), we guess a certain number of secret key bits and apply the meet-in-the-middle attack on multiple ciphertexts. The second attack (TMTO-MTM) is derived from applying the time-memory trade-off attack to the meet-in-the-middle attack on a single ciphertext. We may also use rainbow chains in the table construction to get the Rainbow-MTM attack. The fourth attack (BS-MTM) is defined by combining the time-memory-data trade-off attack proposed by Biryukov and Shamir to the meet-in-the-middle attack on multiple ciphertexts. Lastly, for the final attack (TMD-MTM), we apply the TMTO-Data curve, which demonstrates the general methodology for multiple data trade-offs, to the meet-in-the-middle attack. GDD-MTM requires no pre-processing, but the attack complexity is high while memory requirement is low. In the last four attacks, pre-processing is required but we can achieve lower (faster) online attack complexity at the expense of more memory in comparison with the GDD-MTM attack. To illustrate how the attacks may be used, we applied them in the cryptanalysis of triple DES. In particular, for the BS-MTM attack, we managed to achieve pre-computation and data complexity which are much lower while maintaining almost the same memory and online attack complexity, as compared to a time-memory-data trade-off attack by Biryukov et al. at SAC 2005. In all, our new methodologies offer viable alternatives and provide more flexibility in achieving time-memory-data trade-offs.

Note: This is a re-formatted version of a paper presented at the ICICS 2008 conference. Due to page restrictions, all algorithms and tables in the paper were shifted to the appendix. Here, we shift them back to their respective sections to improve readability.