This work addresses the subject of mathematics education at secondary schools from a current and stimulating point of view intimately related to computational science. Cryptology is a captivating way of introducing into the classroom different mathematical subjects such as functions, matrices, modular arithmetic, combinatorics, equations, statistics and proofs, which usually are recognized as difficult for many students. Special attention is paid here to the concepts of proof and verification through the definition of zero-knowledge cryptographic protocols. Many other different cryptographic and cryptanalytic activities (building and breaking ciphers, respectively) and modern cryptographic applications such as secret-sharing protocols are also proposed as resources for motivating mathematics learning and for achieving a significant improvement in student understanding of several algebraic, analytical and statistical concepts.