Marialaura NOCE | DALLA TEORIA DEI GRUPPI ALLA CRITTOGRAFIA
Marialaura NOCE DALLA TEORIA DEI GRUPPI ALLA CRITTOGRAFIA
cod. 8860300027
DALLA TEORIA DEI GRUPPI ALLA CRITTOGRAFIA
| 8860300027 | |
| DEPARTMENT OF MATHEMATICS | |
| Corso di Dottorato (D.M.226/2021) | |
| MATHEMATICS | |
| 2023/2024 |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2023 | |
| FULL ACADEMIC YEAR |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/02 | 2 | 10 | LESSONS |
| Objectives | |
|---|---|
| THE COURSE IS BASED ON PROVIDING THE MAIN APPLICATIONS OF GROUP THEORY TO CRYPTOGRAPHY. THE MAIN OBJECTIVE OF THE COURSE IS TO PROVIDE BASIC IDEAS TO TACKLE THE STUDY OF GROUP-BASED CRYPTOGRAPHY AND THE CONNECTIONS BETWEEN GROUPS AND CRYPTOGRAPHY. |
| Prerequisites | |
|---|---|
| UNDERGRADUATE GROUP THEORY. |
| Contents | |
|---|---|
| CRYPTOGRAPHY IS DEFINED AS THE METHOD TO PROTECT INFORMATION AND COMMUNICATION. THROUGHOUT THE CENTURIES, MANY CRYPTOGRAPHIC METHODS HAVE BEEN DEVELOPED, AND ALMOST ALL SHARE A COMMON FOUNDATION: THE RESOLUTION OF A MATHEMATICAL PROBLEM. MANY OF THESE METHODS ARE BASED ON APPLICATIONS OF NUMBER THEORY; HOWEVER, IN RECENT DECADES, CRYPTOGRAPHIC SYSTEMS BASED ON GROUP THEORY HAVE BEGUN TO BE STUDIED. CRYPTOGRAPHY BASED ON GROUPS IS INDEED A VERY RECENT AND RAPIDLY GROWING RESEARCH FIELD THAT LIES AT THE INTERSECTION OF GROUP THEORY, COMBINATORICS, COMPLEXITY THEORY, CODE THEORY, AND CRYPTOLOGY. IN THIS COURSE, WE PRESENT SEVERAL WELL-KNOWN CRYPTOGRAPHIC PROTOCOLS, SUCH AS DIFFIE-HELLMAN, KO-LEE, AND ANSHEL-ANSHEL-GOLDFELD. AFTER THAT, WE SURVEY ELEMENTARY TOPICS IN COMBINATORIAL GROUP THEORY AND COMPLEXITY THEORY. THEN, WE DESCRIBE ALGORITHMIC PROBLEMS ARISING FROM GROUP THEORY, TOGETHER WITH CRYPTOGRAPHIC PROTOCOLS BASED ON THESE PROBLEMS. THE FINAL PART OF THE COURSE WILL FOCUS ON PRESENTING SOME CLASSES OF GROUPS AND THEIR SUITABILITY AS PLATFORMS FOR BOTH CLASSICAL AND QUANTUM CRYPTOGRAPHY. |
| Teaching Methods | |
|---|---|
| THE COURSE CONSISTS OF 10 HOURS OF CLASSROOM TEACHING. IN THE LECTURES, THE COURSE TOPICS ARE PRESENTED FOLLOWING THE HISTORICAL DEVELOPMENT OF THE DISCIPLINE. WHILE ATTENDANCE IS NOT MANDATORY, IT IS HIGHLY RECOMMENDED, ESPECIALLY FOR THE EXERCISES. ADDITIONALLY, STUDENTS HAVE THE OPPORTUNITY TO USE THE LECTURER’S DEDICATED WEBPAGE TO DOWNLOAD EDUCATIONAL MATERIALS (PROBLEMS AND REFERENCE TEXTS) AND TO GATHER INFORMATION ABOUT THE TOPICS COVERED IN CLASS. |
| Verification of learning | |
|---|---|
| THE EXAM IS AIMED AT ASSESSING THE UNDERSTANDING OF THE FUNDAMENTAL PRINCIPLES OF GROUP THEORY APPLIED TO CRYPTOGRAPHY. THE EXAM IS BASED ON A SEMINAR ON A PROPOSED TOPIC. THE SEMINAR, DESIGNED TO EVALUATE THE LEVEL OF UNDERSTANDING OF THE TOPICS COVERED IN THE LECTURES, INVOLVES PRESENTING A CRYPTOGRAPHIC PROTOCOL APPLIED TO A CLASS OF GROUPS. THE EVALUATION OF THE SEMINAR WILL TAKE INTO ACCOUNT THE ABILITY TO IDENTIFY THE MOST APPROPRIATE STRATEGIES TO ANALYZE THE TOPICS OF THE COURSE, THE ABILITY TO CLEARLY AND SUCCINCTLY PRESENT THE OBJECTIVES AND THE RESULTS OF THE ELABORATIONS CARRIED OUT, AS WELL AS THE ABILITY TO DEEPEN THE TOPICS COVERED, NAVIGATING APPROPRIATELY AMONG THE MATERIALS PROVIDED. THE MINIMUM EVALUATION LEVEL IS ASSIGNED WHEN THE STUDENT DEMONSTRATES UNCERTAINTIES IN THE APPLICATION OF THE FOUNDATIONAL CONCEPTS OF GROUP THEORY AND CRYPTOGRAPHY, SHOWING LIMITED KNOWLEDGE OF THE BASIC TOPICS AND POOR PRESENTATION SKILLS. THE MAXIMUM LEVEL IS ASSIGNED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND THOROUGH KNOWLEDGE OF THE CONCEPTS AND METHODS OF GROUP THEORY APPLIED TO CRYPTOGRAPHY AND SHOWS A REMARKABLE ABILITY TO CONNECT AND PRESENT THE PROPERTIES OF DIFFERENT TOPICS. |
| Texts | |
|---|---|
| [1] C. BATTARBEE, R. FLORES, MAGGIE E. HABEEB, D. KAHROBAEI, M. NOCE, "APPLICATIONS OF GROUP THEORY IN CRYPTOGRAPHY: POST-QUANTUM GROUP-BASED CRYPTOGRAPHY", MATHEMATICAL SURVEYS AND MONOGRAPHS OF THE AMERICAN MATHEMATICAL SOCIETY (2023). [2] M. I. GONZÁLEZ VASCO, S. MAGLIVERAS, R. STEINWANDT, "GROUP-THEORETIC CRYPTOGRAPHY", CHAPMAN & HALL CRC PRESS, TAYLOR & FRANCIS GROUP (2015). [3] A. MYASNIKOV, V. SHPILRAIN, A. USHAKOV, "GROUP-BASED CRYPTOGRAPHY", ADVANCED COURSES IN MATHEMATICS CRM BARCELONA (2008). |
| More Information | |
|---|---|
| THE LECTURER CAN BE CONTACTED AT THE FOLLOWING EMAIL ADDRESS: MNOCE@UNISA.IT. ADDITIONALLY, A DEDICATED PAGE WILL BE ACTIVE ON: HTTPS://SITES.GOOGLE.COM/VIEW/MARIALAURANOCE/TEACHING/PHD-COURSE-DALLA-TEORIA-DEI-GRUPPI-ALLA-CRITTOGRAFIA. |
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