Multivariate public key cryptosystems (MPKC) is a fast-developing new area in cryptography. In the past 10 years, MPKC schemes have increasingly been seen as a possible alternative to number theoretic-based cryptosystems such as RSA, as they are generally more efficient in terms of computational effort. As quantum computers are developed, MPKC will become a necessary alternative. Multivariate Public Key Cryptosystems systematically presents the subject matter for a broad audience. The first chapter is an introduction to the basic ideas and early development of both multivariate public key cryptography and signature schemes.A The next five chapters deal with the main families of multivariate schemes, and the concept of perturbation, the means by which the security of various schemes can be improved without much cost in efficiency.A Each family is introduced in terms of the origin of the mathematical idea behind its construction, followed by generalizations and related attacks...

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