Improved Order Computation in Class Groups of Real Quadratic Fields

Cryptography is an important tool for safeguarding our data from attackers. The security of several modern cryptosystems relies on unproven properties of an algebraic structure called the class group of an algebraic number field. In the absence of proofs, tabulating class groups in order to generate numerical evidence of these unproven properties remains the best way to enhance our confidence in their truth and the security of the related cryptosystems. However, tabulating class groups in all but the simplest types of number fields remains a significant computational challenge. This project will devise improved algorithms for computing the order of an element in the class group of a real quadratic field, the simplest case of number fields where these challenges manifest. Order computation can be considered as a special case of computing the full class group. The results will be a significant step to improving algorithms for class group computation, eventually leading to the extended class group tabulations required to bolster our confidence in security claims of related cryptosystems.

Faculty Supervisor:

Michael John Jacobson

Student:

Partner:

SRM University-AP

Discipline:

Computer science

Sector:

Cyber Security

University:

University of Calgary

Program: