Efficient Dissection of Bicomposite Problems with Cryptanalytic Applications

Itai Dinur, Orr Dunkelman, Nathan Keller, and Adi Shamir

Abstract

In this paper we show that a large class of diverse problems have a bicomposite structure which makes it possible to solve them with a new type of algorithm called {\it dissection}, which has much better time/memory tradeoffs than previously known algorithms. A typical example is the problem of finding the key of multiple encryption schemes with $r$ independent $n$-bit keys. All the previous error-free attacks required time $T$ and memory $M$ satisfying $TM = 2^{rn}$, and even if false negatives'' are allowed, no attack could achieve $TM<2^{3rn/4}$. Our new technique yields the first algorithm which never errs and finds all the possible keys with a smaller product of $TM$, such as $T=2^{4n}$ time and $M=2^{n}$ memory for breaking the sequential execution of r=7 block ciphers. The improvement ratio we obtain increases in an unbounded way as $r$ increases, and if we allow algorithms which can sometimes miss solutions, we can get even better tradeoffs by combining our dissection technique with parallel collision search. To demonstrate the generality of the new dissection technique, we show how to use it in a generic way in order to improve rebound attacks on hash functions and to solve with better time complexities (for small memory complexities) hard combinatorial search problems, such as the well known knapsack problem.

Available format(s)
Category
Secret-key cryptography
Publication info
A major revision of an IACR publication in CRYPTO 2012
Keywords
Bicomposite problemsdissection algorithmtime-memory tradeoffcryptanalysismultiple encryptionknapsack problems
Contact author(s)
dinuri @ cs bgu ac il
History
2019-06-20: revised
See all versions
Short URL
https://ia.cr/2012/217

CC BY

BibTeX

@misc{cryptoeprint:2012/217,
author = {Itai Dinur and Orr Dunkelman and Nathan Keller and Adi Shamir},
title = {Efficient Dissection of Bicomposite Problems with Cryptanalytic Applications},
howpublished = {Cryptology ePrint Archive, Paper 2012/217},
year = {2012},
note = {\url{https://eprint.iacr.org/2012/217}},
url = {https://eprint.iacr.org/2012/217}
}

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