Understanding Lattice-Based Cryptography Concepts

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The Short Integer Solutions (SIS) Problem involves defining its notation and conditions for solution existence, illustrated with a simple example. SIS is pivotal in constructing collision-resistant hashes and relates to the ISIS problem, which has specific solvability conditions. The equivalence of SIS and ISIS is established. Furthermore, the normal-form ISIS problem is defined, highlighting its connection to ISIS, and demonstrating equivalence through invertible transformations.