For the Baltimore 2003 meeting of the A.M.S. Daniel Lieman organized an
expository and tutorial conference on public-key cryptography for mathematicians.
This volume is the collection of papers that grew out of that conference.
By contrast to a number of lower-level introductory texts aimed at undergrad-
uates, and which therefore necessarily dilute discussion of specific cryptographic
issues with discussion of elementary mathematics, the aim here was to provide a
survey and introduction to public-key cryptography assuming considerable math-
ematical maturity and considerable general mathematical knowledge. Thus, we
hoped to make clearer the cryptographic issues that fall outside the scope of stan-
dard or typical mathematics.
The papers are mostly expository, with the mathematical level of the exposi-
tion meant to be palatable to experienced mathematicians not already too much
acquainted with this subject.
An important part of the context is the extra-mathematical aspect. That is,
many motivations and crucial issues for genuine cryptography are difficult or im-
possible to understood purely in terms of formal algorithmic or other mathematical
notions. (And the very validity of that last assertion is a subject of debate.) It
is necessary to have some idea of the complications entailed by real-life implemen-
tations of cryptographic systems. In particular, and in considerable contrast to
formal mathematics, we cannot assume that everyone plays by the rules. Further,
indeed, by contrast to most mathematical and scientific research contexts wherein
there is no antagonist other than a merely disinterested Nature, the presence of an
active antagonist is a singular aspect of the practice of cryptography.
Some of the authors of the papers are academic mathematicians, some are pro-
fessional cryptographers outside academe, and some have been in both situations.
All the papers were reviewed for literal correctness and for aptness for our espoused
Paul Garrett
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