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Group-based Cryptography (Paperback, 2008 ed.)
Loot Price: R1,428
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Group-based Cryptography (Paperback, 2008 ed.)
Series: Advanced Courses in Mathematics - CRM Barcelona
Expected to ship within 10 - 15 working days
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This book is about relations between three di?erent areas of
mathematics and theoreticalcomputer science: combinatorialgroup
theory, cryptography, and c- plexity theory. We
explorehownon-commutative(in?nite) groups, which arety-
callystudiedincombinatorialgrouptheory,
canbeusedinpublickeycryptography. We also show that there is a
remarkable feedback from cryptography to com- natorial group theory
because some of the problems motivated by cryptography appear to be
new to group theory, and they open many interesting research -
enues within group theory. Then, we employ complexity theory,
notably generic case complexity of algorithms, for cryptanalysisof
various cryptographicprotocols based on in?nite groups. We also use
the ideas and machinery from the theory of generic case complexity
to study asymptotically dominant properties of some in?nite groups
that have been used in public key cryptography so far. It turns out
that for a relevant cryptographic scheme to be secure, it is
essential that keys are selected from a "very small" (relative to
the whole group, say) subset rather than from the whole group.
Detecting these subsets ("black holes") for a part- ular
cryptographic scheme is usually a very challenging problem, but it
holds the keyto creatingsecurecryptographicprimitives
basedonin?nite non-commutative groups. The book isbased onlecture
notesfor the Advanced Courseon Group-Based
CryptographyheldattheCRM, BarcelonainMay2007.
Itisagreatpleasureforus to thank Manuel Castellet, the
HonoraryDirector of the CRM, for supporting the idea of this
Advanced Course. We are also grateful to the current CRM Director,
JoaquimBruna, and to the friendly CRM sta?, especially Mrs. N.
PortetandMrs. N. Hern andez, for their help in running the Advanced
Course and in preparing the lecture notes."
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