COLLOQUIUM

강연주제: Combinatorics and Geometry in Cryptography: Mathematics at Play

강연일시: 2026.9.17.(목) 16:30-17:30

강연장소: 제 1과학관 31351A호

강연자: 최원석 교수 (DGIST 전기전자컴퓨터공학과)

Cryptography is often first encountered through number theory: prime numbers, modular arithmetic, and RSA. Modern cryptography, however, draws on a much wider range of mathematics. In this talk, I will present two examples in which questions about security and privacy are transformed into problems in combinatorics and geometry.

The first example is Patarin’s mirror theory. Here, proving that an idealized cipher behaves like a truly random object becomes a counting problem: how many solutions does a system of equations over a finite group have when certain variables are required to remain pairwise distinct?

The second example comes from secure two-party computation. Alice and Bob wish to compute a joint answer from their private inputs without revealing unnecessary information to each other. Recent work encodes possible protocols as points in a high-dimensional Euclidean space. Communication is represented using constrained convex combinations, and deciding whether a protocol exists becomes a geometric membership problem. In small examples, impossibility can literally become a picture one can draw.