USF Center for Cryptographic Research

Research Training Group

Applied Algebra at the USF

The Center for Cryptographic Research (CCR) runs a Research Training Group (RTG) program on the topic of Applied Algebra. It is a vertically integrated training program bringing together faculty, postdoctoral fellows, graduate students and undergraduate students. The research projects are divided into 3 main trusts: 

  • Mathematical Cryptography.
  • Error Correcting Codes.
  • Quantum Computing.

The Applied Algebra RTG includes a variety of programs on the topics of cryptography, coding theory, and quantum computing at all levels. The mathematics PhD degree includes an applied algebra elective sequence, while a 12 credit undergraduate certificate program on Cryptography is available to mathematics and computer science majors. Each year in the summer, the CCR organizes a 10 week REU Site program where undergraduates from all over the nation participate in research in Applied Algebra. The RTG program is also connected to the USF Quantum Initiative which has developed quantum computing courses within 4 different departments (Computer Science & Engineering, Electrical Engineering, Mathematics, and Physics). The RTG program also includes a cybersecurity summer program for young girls “The CodeBreakHERs”. 

Additionally, the RTG program offers a variety of professional developments to its trainees. A multi-tier mentoring system allows undergraduate and graduate trainees to be mentored by a postdoctoral scholar, while cross-cohort peer tutoring allows senior trainees to mentor more junior ones. In monthly meetings, all members engage in collaborative problem solving, idea sharing, and networking. Postdoctoral and graduate trainees also benefit from regular workshops to improve their teaching skills in collaboration with the USF College of Education. Trainees also benefit from opportunities to work on leadership, communication, and writing skills. Finally, the RTG program includes the creation of the Florida Hub for Applied Algebra which consists in the organization of 4 workshops per year (3 at the University of South Florida, and 1 at the Florida Atlantic University). Each workshop brings together Applied Algebra scientists from the Florida State University System, as well as external invited speakers. 

If you are interested in joining our RTG as an undergraduate, graduate or postdoctoral trainee, please fill out the interest form below:

Interest Form

Cryptography

This RTG program includes research projects on the mathematics of cryptography. In particular, the participants will have the possibility to learn about modern asymmetric encryption schemes based on Euclidean lattices, isogenies, and error correcting codes. These new types of primitives are the subject of extremely active research at the intersection between theoretical computer science and pure mathematics. The participants will also have the opportunity to explore the connections between pure mathematics and block cipher design through so-called Almost Perfect Nonlinear functions. These are connected to computational Galois theory, which is an exciting area of research in computational algebra.

Coding Theory

Error correcting codes are used to protect communications from information loss during transmission. They are also used in cloud storage to solve the so-called “repair problem”, which is when errors occur in a known location of the data. Typically, when a given server becomes unavailable (due to a crash, maintenance, etc …). The kinds of codes used to solve the repair problem are called “locally recoverable codes”. During this program, the participants will have the opportunity to participate in research on the design of optimal locally recoverable codes. They will leverage deep connection between these objects and computational algebra and Galois theory. 

Quantum Computing

The recent developments of quantum information science and quantum computing suggest that this field will significantly impact the industrial and academic landscape in the near future. This RTG program leverages synergies with cryptography, coding theory, physics, and fundamental notions of computational algebra and number theory. The proposed research topics in quantum computing include computational algebra problem to approximate unitary matrices and their applications to quantum circuit design, quantum error correcting codes, and quantum algorithms for the resolution of computational problem in algebra (with a focus on those relevant to the security of cryptographic schemes). 

Postdoc/Grad trainees

This RTG program supports 3 postdoctoral scholars, and 3 graduate students working on research topics in line with the 3 main thrusts outlined above. Postdoctoral scholars and graduate students benefit from numerous professional development opportunities, including  a multi-tier mentoring system and cross-cohort peer tutoring. Additionally, regular workshops to enhance teaching, speaking and writing skills are organized. RTG trainees have access to lab space containing A/V system, a 64 core computing station, a computer room, breakout rooms, and hot desks. 

UG Trainees (REU)

Undergraduate research is an important component of this RTG program. It supports 6 participants that perform research alongside with faculty, postdoctoral and graduate trainees, as well as 10 participants coming for an intensive 10-week long summer program (REU Site). The Research Experience Undergraduate is a stepping stone to graduate school. The program aims to offer its participants a first experience in research. In addition, participants get to expand their network with USF faculty and their summer guests ahead of graduate school applicants.

Applied Algebra Days

This RTG sponsors the workshop series “Applied Algebra Days”. Every year, 4 workshops on Applied Algebra are organized (3 at the University of South Florida, and 1 at Florida Atlantic University). These workshop bring together faculty, postdocs and students from the Florida State University System doing research in Applied Algebra, as well as out-of-state guest lecturers. These workshops are a valuable resource to help the RTG trainees learn about current research trends, present their ongoing research, and expand their scientific network. 

K-12 Outreach

This RTG program includes outreach to K-12 students with the intend to boost participation of women and underrepresented minorities in Applied Algebra. In particular, faculty and trainees participate in the preparation and the organization of the CodeBreakHERs: a weeklong summer program on cybersecurity for Grade 8-12 girls. This program consists in hands on activities on topics including cryptography, error correcting codes, internet security, hardware security, and visits from real life CodeBreakHERs who engage with the participants during a round table event.