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Non commutative groups, specially Braid groups of Artin in recent years have emerged as suitable setting for cryptographic protocols. The idea of using the braid group as a platform for cryptosystems was first introduced in 1999 by Anshel, Anshel and Goldfeld. The useful feature of Braid groups is that they are more complicated than Abelian groups, but are not too complicated to work with. These two characteristics make braid group a convenient and suitable choice. However, recent results about the linearity of braid groups and Lawrence-Krammer representations have made these cryptosystems vulnerable to linear algebra based attacks.
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