Algebraic aspects of multivariate cryptosystems based on tame transformations
Cryptography has its roots in Mathematics and Computer Science, and recently has been one of the most visible branches of “applied mathematics”—it serves an eminently useful and very critically important purpose in an electronically connected world. It is hard to over-stress the significance of a fast and secure digital signature scheme. TTS (Tame Transformation Signature), our current work in progress, provides such a digital signature scheme. ^ We introduce TTS, a realization of T. Moh's theory on using the multivariate public-key cryptosystem TTM (Tame Transformation Method) for digital signatures. We describe the principles behind TTS, then we give a detailed view of how well an extant TTS implementation performs, and stands up to previously known attacks. Based on this topical assessment, we still consider TTS competitive or superior in several aspects to other schemes, partly because TTS and TTM share the theoretical roots of Tame Transformations, and hence many good traits including high security, ease of implementation and good execution speed. ^ Although we concentrate on algebraic aspects of TTS signature scheme in this dissertation, most theory and discussions apply to TTM cryptosystem for encryption and decryption as well. ^
Major Professor: Tzuong-Tsieng Moh, Purdue University.