Memoryless Unbalanced Meet-in-the-Middle Attacks: Impossible Results and Applications

  • Yu Sasaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8479)

Abstract

A meet-in-the-middle (MitM) attack is a popular tool for cryptanalysis. It independently computes two functions \(\mathcal{F}\) and \(\mathcal{G}\), and finds a match of their outputs. When the cost of computing \(\mathcal{F}\) and \(\mathcal{G}\) are different, the problem is called unbalanced MitM attack. It is known that, for the balanced case, the MitM attack can be performed only with a negligible memory size without significantly increasing the computational cost by using the Floyd’s cycle-finding algorithm. It is also widely believed that the same technique can be applied to the unbalanced case, while no one has shown the evidence of its possibility yet. This paper contains two contributions. Firstly, we show an impossibility of the memoryless unbalanced MitM attack without significantly increasing the computational cost. The conversion to the memoryless attack with the Floyd’s cycle-finding algorithm always requires additional computational cost. Secondly, we find applications of the memoryless unbalanced MitM attack to show that it is still meaningful even with some additional computational cost. It can be used to generate multi-collisions of hash functions by using a dedicated collision attack algorithm. Our method finds 3-collisions of SHA-1 with 2142 computations and negligible memory size, while the known best attack requires 2106.6 computations and 253.3 memory size. The memoryless unbalanced MitM attack can also be applied to the limited-birthday distinguisher for hash functions.

Keywords

unbalanced meet-in-the-middle memoryless attack Floyd’s cycle-finding algorithm hash function SHA-1 3-collision limited-birthday distinguisher 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Yu Sasaki
    • 1
  1. 1.NTT Secure Platform LaboratoriesMusashino-shiJapan

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