11,160 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Impossibility of Three Pass Protocol using Public Abelian Groups
Key transport protocols are designed to transfer a secret key from an
initiating principal to other entities in a network. The three-pass protocol is
a key transport protocol developed by Adi Shamir in 1980 where Alice wants to
transport a secret message to Bob over an insecure channel, and they do not
have any pre-shared secret information. In this paper, we prove the
impossibility of secret key transportation from a principal to another entity
in a network by using the three pass protocol over public Abelian groups. If it
were possible to employ public Abelian groups to implement the three-pass
protocol, we could use it in post-quantum cryptography for transporting keys
providing information theoretic security without relying on any computationally
difficult problem
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
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