Collaborative Research: CT-ISG: Efficient Cryptography Based on Lattices

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Only two number-theoretic assumptions --- hardness of factoring and ofcomputing discrete logarithms --- underlie essentially all public-keycryptosystems in widespread use today. For lower-level primitivessuch as hash functions, random number generators, and stream ciphers,the situation is even worse: existing provably-secure constructionsare too inefficient to compete with practical alternatives such asSHA-1 or AES, and so the primitives in use today have no rigorousjustification for their security. This research will investigate new classes of computationalassumptions based on lattices. Based on these assumptions, theinvestigators will seek to design cryptographic primitives that areboth provably secure and comparably efficient to existing, deployedschemes. The research will explore the use of lattices to constructbasic cryptographic primitives, including hash functions, pseudorandomgenerators, shared-key authentication protocols, public-key encryptionschemes (including those secure against chosen-ciphertext attacks),and digital signatures. The educational component of this work willfocus on educating graduate students as well as developing introductory-level surveys of lattice-based cryptography.