A semiring is an algebraic structure satisfying the usual axioms for a not necessarily commutative ring, but without the requirement that addition be invertible. Aside from rings, well-studied instances in cryptographic applications include the Boolean semiring and the tropical semiring. The latter, in particular, behaves to a large extent like a field and exhibits interesting properties in the cryptographic context. This short note explores a GPU-based highly parallel implementation of a protocol recently proposed by Grigoriev and Shpilrain [Comm. Algebra 42 (2014), 2624–2632], in the context of Diffie–Hellman key agreements.
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