Advisor:  Dr. Rachel Pries

Committee:  Dr. Jamie Juul, Dr. Indrajit Ray

Title:  GR-NTRU: Understanding the Security of Lattice-based Cryptosystems through Group Rings
Originally conceived in 1996 by authors Hoffstein, Pipher, and Silverstein, the Nth-degree Truncated Ring Unit (NTRU) cryptosystem rivals common cryptosystems such as RSA in terms of speed and security. In pursuit of a deeper understanding of NTRU, we explore a generalization of the cryptosystem using group rings, known as GR-NTRU. This perspective allows for the formulation of a new kind of attack on NTRU-like cryptosystems. In particular, via representation theory, one can decompose a group ring into smaller matrix rings. This decomposition can greatly impact the computational complexity of lattice-based attacks on NTRU-like cryptosystems. We present a summary of how this attack affects GR-NTRU for certain classes of groups, and we end with a detailed example for the group S_3.

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