https://www.math.snu.ac.kr/board/files/attach/images/701/ff97c54e6e21a4ae39315f9a12b27314.png
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 .
Atachment
첨부 '1'
  1. 07Nov
    by Editor
    in 특별강연

    A New Approach to Discrete Logarithm with Auxiliary Inputs

  2. A wrapped Fukaya category of knot complement and hyperbolic knot

  3. Algebraic surfaces with minimal topological invariants

  4. Combinatorics and Hodge theory

  5. Contact topology and the three-body problem

  6. Harmonic bundles and Toda lattices with opposite sign

  7. Irreducible Plane Curve Singularities

  8. Mathematical Analysis Models and Siumlations

  9. Persistent Homology

  10. Queer Lie Superalgebras

  11. Regularity of solutions of Hamilton-Jacobi equation on a domain

  12. Regularization by noise in nonlinear evolution equations

  13. Structures on Persistence Barcodes and Generalized Persistence

  14. Topological Mapping of Point Cloud Data

  15. What is Weak KAM Theory?

  16. 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

  17. 허준이 교수 호암상 수상 기념 강연 (Lorentzian Polynomials)

Board Pagination Prev 1 Next
/ 1