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A New Key Exchange Primitive Based on the Triple Decomposition Problem
Authors: Yesem KurtAbstract:
We present a new key exchange primitive based on the decomposition problem over non-commutative groups. Different from the key establishment schemes that rely on the decomposition problem where the problem is decomposing an element into three parts where the middle piece is known, our scheme relies on decomposing an element into three parts, all unknown. We call this problem “Triple Decomposition Problem”. This seems to be a harder problem because it requires quadratic systems to be solved instead of linear systems. We discuss the new primitive over two different protocols. The underlying problems in the two protocols differ slightly. We discuss the system and the underlying problems in one of the protocols in detail over braid groups. We manage to provide a setting which resists against linear algebra attacks and length based attacks.
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