For those who would like to get a better idea of the cryptography described in this article, here is an overview of the usually encountered computational hardne

For those who would like to get a better idea of the cryptography described in this article, here is an overview of the usually encountered computational hardness problems in lattice-based cryptography: 1. Shortest Vector Problem (SVP) - Given a lattice with a basis B, find the shortest vector in the lattice. 2. Closest Vector Problem (CVP) - Given a lattice with a basis B and some target vector t, find the point v which is closest to t. 3. Shortest Independent Vector Problem (SIVP) - Given a lattice basis B in Z^(n x n), find n linearly independent lattice vectors [s1, ..., sn], where si is in the lattice of basis B for all i. 4. Learning With Errors (LWE) - Given integral starting parameters n, m and q, with a probability distribution X on Zq, distinguish between an input pair (A, v) and a vector e in (Zq)^m. A is chosen uniformly from (Zq)^(m x n) and v is (typically) chosen uniformly from (Zq)^m. In other words, try to recover the secret key s in (Zq)^n by examining a sequence of approximate linear equations. The error introduced is what makes this computationally hard, otherwise it could be done in polynomial time using Gaussian elimination. 5. Learning Parity With Noise (LPN) - Given a secret length l, a noise rate 0 < r < 0.5 and the number of samples q, find the random l-bit secret string s in (Z2)^l using q samples. This is the search problem version; there is also a decisional variant. There are good surveys that cover lattice-based cryptography in general or particular computational problems in greater depth; for example, try [1], [2], or [3]. ________________________________________ 1. Peikert, Chris: A Decade of Lattice-Based Cryptography - https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf https://web.eecs.umich.edu/~cpeikert/pubs/lattice-survey.pdf 2. Micciancio, Regev: Lattice-Based Cryptography (chapter in Post-Quantum Cryptography) 3. Regev, Oded: The Learning With Errors Problem - https://cims.nyu.edu/~regev/papers/lwesurvey.pdf https://cims.nyu.edu/~regev/papers/lwesurvey.pdf