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- Alex D. Myasnikov, Alexander Ushakov
- Public Key Cryptography
- 2007

The length based attack on Anshel-Anshel-Goldfeld commutator key-exchange protocol [1] was initially proposed by Hughes and Tannenbaum in [9]. Several attempts have been made to implement the attack [6], but none of them had produced results convincing enough to believe that attack works. In this paper we show that accurately designed length based attack… (More)

- Alex D. Myasnikov, Alexander Ushakov
- Groups Complexity Cryptology
- 2009

The Anshel-Anshel-Goldfeld-Lemieux (abbreviated AAGL) key agreement protocol [1] is proposed to be used on low-cost platforms which constraint the use of computational resources. The core of the protocol is the concept of an Algebraic Eraser (abbreviated AE) which is claimed to be a suitable primitive for use within lightweight cryptography. The AE… (More)

- Alex D. Myasnikov
- Groups Complexity Cryptology
- 2009

Generic case complexity has originated about a decade ago in combinatorial group theory [10, 2]. This area has long computational traditions with many fundamental problems being algorithmic in nature. It has been shown that most computational problems in infinite group theory are recursively undecidable. However, it was also observed that decision… (More)

- Alex D. Myasnikov, Alexander Ushakov
- IACR Cryptology ePrint Archive
- 2012

We propose a polynomial time quantum algorithm for solving the discrete logarithm problem in matrices over finite group rings. The hardness of this problem was recently employed in the design of a key-exchange protocol proposed by D. Kahrobaei, C. Koupparis, and V. Shpilrain [4]. Our result implies that the Kahrobaei et al. protocol does not belong to the… (More)

This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity applies to both recursively solvable and recursively unsolvable problems.

- Alex D. Myasnikov, Alexander Ushakov
- IACR Cryptology ePrint Archive
- 2012

In this paper we cryptanalyze two protocols: GrigorievShpilrain authentication protocol and Wang et al. public key encryption protocols that use computational hardness of some variations of the conjugacy search problem in noncommutative monoids. We devise a practical heuristic algorithm solving those problems. As a conclusion we claim that these protocols… (More)

- M. Kreuzer, Alex D. Myasnikov, Alexander Ushakov
- ACNS
- 2014

The Anshel-Anshel-Goldfeld-Lemieux (abbreviated AAGL) key agreement protocol [2] is proposed to be used on low-cost platforms which constraint the use of computational resources. The core of the protocol is the concept of an Algebraic Eraser (abbreviated AE) which is claimed to be a suitable primitive for use within lightweight cryptography. The AE… (More)

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