Backgrounds

Those who want to step inside (lattice-based) cryptography should read the following references for background:

• Theory of computation:

  • MIT Opencourse by Michael Sipser (his book is here)

• Theory of Complexity:

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• Foundations of Cryptography:

  • Goldreich's books Vol 1, Vol 2 (his website)

  • Nigel P Smart books: Cryptography Made Simple

  • Book: A Graduate Course in Applied Cryptography by Dan Boneh and Victor Shoup

• Theory of Lattices:

  • Vinod's course 2020 : CS 294-168 Lattices, Learning with Errors and Post-Quantum Cryptography

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• Cryptographic Protocols:

  • Cryptography and Cryptographic Protocols by Oded Goldreich

  • Lecture Notes Cryptographic Protocols by Berry Schoenmakers

• Security Proofs:

  • Game-based Proof: Sequences of games: a tool for taming complexity in security proofs by Victor Shoup (or here)

  • Simulation-based Proof: How To Simulate It - A Tutorial on the Simulation Proof Technique by Yehuda Lindell

  • UC-based Proof: Universally Composable Security: A New Paradigm for Cryptographic Protocols by Ran Cannetti

  • Security Reduction: [Book] Introduction to Security Reduction by Fuchun Guo, Willy Susilo, Yi Mu

ROM & QROM

• Random Oracles in a Quantum World by Dan Boneh and Özgür Dagdelen and Marc Fischlin and Anja Lehmann and Christian Schaffner and Mark Zhandry

• Random Oracles are Practical: A Paradigm for Designing Ecient Protocols by Mihir Bellare and Phillip Rogawa

• The Random Oracle Model: A Twenty-Year Retrospective by Neal Koblitz and Alfred Menezes

• The Random Oracle Methodology, Revisited by Ran Canetti, Oded Goldreich and Shai Halevi

Choose Parameters for LWE

• LWE Estimator (Documentations): https://lwe-estimator.readthedocs.io/en/latest/

• Script on SageMath:

load("https://bitbucket.org/malb/lwe-estimator/raw/HEAD/estimator.py")

n, alpha, q = 256, 0.000976562500000000, 65537

set_verbose(1)

_ = estimate_lwe(n, alpha, q)

• Estimate all the fLWE, NTRUg schemes: https://estimate-all-the-lwe-ntru-schemes.github.io/docs/