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This collection of articles grew out of an expository and tutorial conference on public-key cryptography held at the Joint Mathematics Meetings (Baltimore). The book provides an introduction and survey on public-key cryptography for those with considerable mathematical maturity and general mathematical knowledge. Its goal is to bring visibility to the cryptographic issues that fall outside the scope of standard mathematics. These mathematical expositions are intended for experienced mathematicians who are not well acquainted with the subject. The book is suitable for graduate students, researchers, and engineers interested in mathematical aspects and applications of public-key cryptography.