255 research outputs found
A note on strong protomodularity, actions and quotients
In order to study the problems of extending an action along a quotient of the
acted object and along a quotient of the acting object, we investigate some
properties of the fibration of points. In fact, we obtain a characterization of
protomodular categories among quasi-pointed regular ones, and, in the
semi-abelian case, a characterization of strong protomodular categories.
Eventually, we return to the initial questions by stating the results in terms
of internal actions
Bourn-normal monomorphisms in regular Mal'tsev categories
Normal monomorphisms in the sense of Bourn describe the equivalence classes
of an internal equivalence relation. Although the definition is given in the
fairly general setting of a category with finite limits, later investigations
on this subject often focus on protomodular settings, where normality becomes a
property. This paper clarifies the connections between internal equivalence
relations and Bourn-normal monomorphisms in regular Mal'tesv categories with
pushouts of split monomorphisms along arbitrary morphisms, whereas a full
description is achieved for quasi-pointed regular Mal'tsev categories with
pushouts of split monomorphisms along arbitrary morphisms.Comment: This vesion fixes one error present in the last section of the
previous versio
Automated Cryptographic Analysis of the Pedersen Commitment Scheme
Aiming for strong security assurance, recently there has been an increasing
interest in formal verification of cryptographic constructions. This paper
presents a mechanised formal verification of the popular Pedersen commitment
protocol, proving its security properties of correctness, perfect hiding, and
computational binding. To formally verify the protocol, we extended the theory
of EasyCrypt, a framework which allows for reasoning in the computational
model, to support the discrete logarithm and an abstraction of commitment
protocols. Commitments are building blocks of many cryptographic constructions,
for example, verifiable secret sharing, zero-knowledge proofs, and e-voting.
Our work paves the way for the verification of those more complex
constructions.Comment: 12 pages, conference MMM-ACNS 201
The snail lemma for internal groupoids
We establish a generalized form both of the Gabriel-Zisman exact sequence associated with a pointed functor between pointed groupoids, and of the Brown exact sequence associated with a fibration of pointed groupoids. Our generalization consists in replacing pointed groupoids with groupoids internal to a pointed regular category with reflexive coequalizer
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