Cryptography

Objectives

The Cryptography course delves into the theoretical foundations that support modern cryptography. The aim is to formally capture the intended security notions, and achieve familiarity with the algebraic structures and number theory that underpin the latest cryptographic techniques, as well as proficiency with the computational tools that implement these structures. Thus, at the end, students will be able to:

  • Classify different crypto-analysis attacks, such as known-plaintext; chosen-plaintext; chosen-ciphertext; man-in-the-middle and brute force;
  • Establish the security of a cryptographic system with respect to a security model (security objective/attacker model/security proof);
  • Develop knowledge of the fundamentals of algebra and number theory that underpin the “hard problems” supporting the security of current cryptographic techniques, both in classic and quantum computing scenarios;
  • Perform security proofs of cryptographic primitives based on reduction arguments to hard-problems;
  • Reason about the security of cryptographic protocols (e.g. multiparty computation (MPC) protocols; zero-knowledge (ZK) proofs).

Program

  • Security formalization in cryptographic systems: absolute and computational security; security models for different security objectives (e.g. confidentiality; integrity; authenticity);
  • Mathematical foundations: discrete probabilities; formal logic; concepts of algebra and number theory;
  • Security proofs: reduction arguments (game-hoping); security assumptions (hard problems); attacker models; examples of proofs or counterarguments of the various families of cryptographic primitives;
  • Cryptographic protocols: secure multiparty computation (MPC); simulation paradigm; zero-knowledge proofs.

Bibliography

  • Jeffrey Hoffstein, Jill Pipher & Joseph H. Silverman. “An Introduction to Mathematical Cryptography”. Undergratuate Texts in Mathematics; Springer, 2010.
  • Dan Boneh, Victor Shoup. “A Graduate Course in Applied Cryptography”. Draft book available at http://toc.cryptobook.us
  • J.M.E.Valença. “Lições de Criptografia”. apontamentos manuscritos.

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