180 research outputs found
Public key exchange using semidirect product of (semi)groups
In this paper, we describe a brand new key exchange protocol based on a
semidirect product of (semi)groups (more specifically, on extension of a
(semi)group by automorphisms), and then focus on practical instances of this
general idea. Our protocol can be based on any group, in particular on any
non-commutative group. One of its special cases is the standard Diffie-Hellman
protocol, which is based on a cyclic group. However, when our protocol is used
with a non-commutative (semi)group, it acquires several useful features that
make it compare favorably to the Diffie-Hellman protocol. Here we also suggest
a particular non-commutative semigroup (of matrices) as the platform and show
that security of the relevant protocol is based on a quite different assumption
compared to that of the standard Diffie-Hellman protocol.Comment: 12 page
Tropical cryptography II: extensions by homomorphisms
We use extensions of tropical algebras as platforms for very efficient public
key exchange protocols.Comment: 7 pages. arXiv admin note: text overlap with arXiv:1301.119
SPDH-Sign: towards Efficient, Post-quantum Group-based Signatures
In this paper, we present a new diverse class of post-quantum group-based
Digital Signature Schemes (DSS). The approach is significantly different from
previous examples of group-based digital signatures and adopts the framework of
group action-based cryptography: we show that each finite group defines a group
action relative to the semidirect product of the group by its automorphism
group, and give security bounds on the resulting signature scheme in terms of
the group-theoretic computational problem known as the Semidirect Discrete
Logarithm Problem (SDLP). Crucially, we make progress towards being able to
efficiently compute the novel group action, and give an example of a
parameterised family of groups for which the group action can be computed for
any parameters, thereby negating the need for expensive offline computation or
inclusion of redundancy required in other schemes of this type
Some applications of noncommutative groups and semigroups to information security
We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL2(Fp), and compute bounds on the girth of the Cayley graph of the subgroup of SL2(Fp) for specific generators A, B. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family
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