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تسجيل مستخدم جديدA Practical Cryptanalysis of the Algebraic Eraser
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Anshel, Anshel, Goldfeld and Lemieaux introduced the Colored Burau Key Agreement Protocol (CBKAP) as the concrete instantiation of their Algebraic Eraser scheme. This scheme, based on techniques from permutation groups, matrix groups and braid groups, is designed for lightweight environments such as RFID tags and other IoT applications. It is proposed as an underlying technology for ISO/IEC 29167-20. SecureRF, the company owning the trademark Algebraic Eraser, has presented the scheme to the IRTF with a view towards standardisation. We present a novel cryptanalysis of this scheme. For parameter sizes corresponding to claimed 128-bit security, our implementation recovers the shared key using less than 8 CPU hours, and less than 64MB of memory.
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On March 2004, Anshel, Anshel, Goldfeld, and Lemieux introduced the emph{Algebraic Eraser} scheme for key agreement over an insecure channel, using a novel hybrid of infinite and finite noncommutative groups. They also introduced the emph{Colored Bur
au Key Agreement Protocol (CBKAP)}, a concrete realization of this scheme. We present general, efficient heuristic algorithms, which extract the shared key out of the public information provided by CBKAP. These algorithms are, according to heuristic reasoning and according to massive experiments, successful for all sizes of the security parameters, assuming that the keys are chosen with standard distributions. Our methods come from probabilistic group theory (permutation group actions and expander graphs). In particular, we provide a simple algorithm for finding short expressions of permutations in $S_n$, as products of given random permutations. Heuristically, our algorithm gives expressions of length $O(n^2log n)$, in time and space $O(n^3)$. Moreover, this is provable from emph{the Minimal Cycle Conjecture}, a simply stated hypothesis concerning the uniform distribution on $S_n$. Experiments show that the constants in these estimations are small. This is the first practical algorithm for this problem for $nge 256$. Remark: emph{Algebraic Eraser} is a trademark of SecureRF. The variant of CBKAP actually implemented by SecureRF uses proprietary distributions, and thus our results do not imply its vulnerability. See also arXiv:abs/12020598
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