(... to be written)

Sources

An introduction to lattices and learning with errors is [A12]. A survey of the field of lattice cryptography from 2016 can be found in [P16]. If you want to get your hands dirty and play around, a great C library for experimenting with and prototyping lattice-based cryptography is [OQSP] from the Open Quantum Safe Project [SM16]. A good place to start exploring the field of lattice cryptography is [MLAT].

This crypto bite is inspired by many talks. Oded Regev, the inventor of Learning With Errors (LWE) [R05, R10], an important application of lattices used in cryptography, gave an introduction and broad overview of lattices in his talk "Introduction to Lattices" (slides) at the 2nd BIU Winter School on Cryptography: Lattice-based Cryptography and Applications. February 19-22 2012. (all videos):

Vinod Vaikuntanathan's "Lattices and Cryptography: A Match Made in Heaven" at the PQCrypto 2014 conference is an excellent overview:

There is a whole series of talks on Lattice-based Cryptography at

• The 2nd BIU Winter School on Cryptography: Lattice-based Cryptography and Applications. February 19-22 2012. (all videos).

Literature

• [R05] Oded Regev: On Lattices, Learning with Errors, Random Linear Codes, and Cryptography. In: STOC'05, Proceedings of the thirty-seventh annual ACM symposium on Theory of computing, May 22 - 24, 2005, pages 84-93 (acm.org paywalled, full pdf)
• [R10] Oded Regev: The Learning with Errors Problem. (full pdf)
• [A12] Daniel Apon: An intro to lattices and learning with errors. A way to keep your secrets secret in a post-quantum world. (slides pdf)
• [P16] Chris Peikert: A Decade of Lattice Cryptography. February 17, 2016. (full pdf)
• [SM16] Douglas Stebila, Michele Mosca: Post-Quantum Key Exchange for the Internet and the Open Quantum Safe Project. (iacr 2016/1017, full pdf)
• [OQSP] The Open Quantum Safe Project. (liboqs)
• [MLAT] Daniele Micciancio: Lattice Cryptography Home