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Extra Form
강연자 천정희
소속 서울대학교
date 2013-02-19
Let  be a cyclic group with generator . The discrete logarithm problem with auxiliary inputs (DLPwAI) is asked to find  with auxiliary inputs ,…, . In Eurocrypt 2006, an algorithm is proposed to solve DLPwAI in  when . In this paper, we reduce the DLPwAI to the problems to find polynomials with small value sets or to find efficiently.
In this talk, we propose a new approach to solve DLPwAI concentrating on the behavior of function mapping between the finite fields rather than using an embedding to auxiliary groups. This result shows the relation between the complexity of the algorithm and the number of absolutely irreducible factors of the substitution polynomials, hence enlightens the research on the substitution polynomials.
More precisely, with a polynomial  of degree over , the proposed algorithm shows the complexity  group operations to recover with , where  denotes the number of pairs  such that . As an example using the Dickson polynomial, we reveal  group operations when .
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List of Articles
카테고리 제목 소속 강연자
특별강연 A New Approach to Discrete Logarithm with Auxiliary Inputs file 서울대학교 천정희
수학강연회 정년퇴임 기념강연: Volume Conjecture file 서울대학교 김혁
특별강연 Irreducible Plane Curve Singularities file 서울대학교 강정혁
수학강연회 Subgroups of Mapping Class Groups file 서울대학교 김상현
수학강연회 Randomness of prime numbers file 서울대학교 임선희
수학강연회 Non-commutative Lp-spaces and analysis on quantum spaces file 서울대학교 이훈희
수학강연회 학부생을 위한 ε 강연회: Mathematics from the theory of entanglement file 서울대학교 계승혁
수학강연회 Brownian motion and energy minimizing measure in negative curvature file 서울대학교 임선희
수학강연회 Combinatorial Laplacians on Acyclic Complexes file 서울대학교 국웅
특별강연 Contact topology and the three-body problem file 서울대학교 Otto van Koert
수학강연회 Fefferman's program and Green functions in conformal geometry file 서울대학교 Raphaël Ponge
특별강연 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds file 서울대학교 박종일
수학강연회 Seeded Ising Model for Human Iris Templates and Secure Distributed Iris Recognition file 서울대학교 최형인
수학강연회 Categorification of Donaldson-Thomas invariants file 서울대학교 김영훈
수학강연회 Random conformal geometry of Coulomb gas formalism file 서울대학교 강남규
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Harmonic Analysis (이진봉) file 서울대학교 이진봉
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Regularity for PDEs (수미야) file 서울대학교 수미야
BK21 FOUR Rookies Pitch 2021-2 Rookies Pitch: Representation Theory(장일승) file 서울대학교 장일승
BK21 FOUR Rookies Pitch 2023-1 Symplectic Topology (노경민) file 서울대학교 노경민
수학강연회 <학부생을 위한 ɛ 강연> 기하와 대수의 거울대칭 file 서울대학교 조철현
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