Coursera Spring Sale
40% Off Coursera Plus Annual!
Grab it
Explore the mathematical foundations and cryptographic applications of lattices through this comprehensive lecture series delivered by Joseph H. Silverman from Brown University at the Park City Mathematics Institute. Begin with understanding lattices as discrete subgroups of R^n and examine the fundamental hard lattice problems that form the basis of modern cryptographic security. Delve into lattice reduction techniques and algorithms that attempt to solve these computationally difficult problems, providing insight into both the theoretical challenges and practical limitations. Gain essential background in public key cryptography principles before advancing to the construction and analysis of lattice-based cryptographic systems. Learn how lattices enable the development of public key cryptosystems and digital signature schemes that remain secure against quantum computer attacks, making them crucial for post-quantum cryptography. Master the implementation of lattice-based digital signatures and understand rejection sampling techniques used to ensure security and efficiency. The series progresses systematically through five main lectures, each divided into multiple parts, covering lattice theory fundamentals, reduction algorithms, cryptographic foundations, practical cryptosystem construction, and advanced signature schemes with rejection sampling methods.
