id: 06563076
dt: b
an: 2016f.01346
au: Diekert, Volker; Kufleitner, Manfred; Rosenberger, Gerhard; Hertrampf,
Ulrich
ti: Discrete algebraic methods. Arithmetic, cryptography, automata and groups.
so: De Gruyter Textbook. Berlin: De Gruyter (ISBN 978-3-11-041332-8/pbk;
978-3-11-041333-5/ebook). xii, 342~p. (2016).
py: 2016
pu: Berlin: De Gruyter
la: EN
cc: P15 H45 F65
ut: cryptography; number theoretic algorithms; primality test; elliptic curves;
automata; infinite groups
ci:
li: doi:10.1515/9783110413335
ab: A very successful attempt of creating a consise and â€œautonomous"
presentation of discrete algebraic methods and its applications has
been achieved through this book. It consists of eight chapters from
which the first provides the algebraic structures needed as the
foundations of the rest of the book. The next seven chapters define the
applications of discrete algebraic methods as a future-oriented topic
containing: cryptography, number theoretic algorithms, polynomial time
primality test, elliptic curves, combinatorics on words, automata and
discrete infinite groups. A remarquable achievement of the authors is
that they do not just provide structured knowledged on the topic, but
they pose questions and give specific answers. Should we use unproven
security claims? Does it make sense to build cryptosystems on NP-hard
problems? Why computations with elliptic curves are necessary?
Moreover, areas of theoretical computer science are approached, for
example at the chapter on automata or the algorithmic branch of
combinatorial group theory at the final chapter. Mathematicians and
computer scientists will surely enjoy the density of presentation of
the various topics of the book.
rv: Panayiotis Vlamos (Athena)