Past Seminars- Cryptography

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  • TBA
    Tue May 30, 2017
    2:00 pm
  • Alice Silverberg and Shahed Sharif
    Tue May 30, 2017
    2:00 pm
    A.S. will give some remarks (joint work with Hendrik Lenstra) on homomorphic encryption schemes of Smart-Vercauteren and Gentry-Halevi. S.S. will discuss the paper "A subfield lattice attack on overstretched NTRU assumptions: Cryptanalysis of some FHE and Graded Encoding Schemes" by Martin Albrecht, Shi Bai, Léo Ducas,...
  • Shahed Sharif
    Mon May 22, 2017
    3:00 pm
    We will complete our discussion of the quantum algorithm to compute the unit group of a number field. We will then discuss applications by Biasse and Song to compute class groups and generators of principal ideals. The paper of Biasse and Song is available on my webpage, http://public.csusm.edu/ssharif/crypto
  • Shahed Sharif
    Mon May 15, 2017
    3:00 pm
    We will discuss the quantum Fourier transform for an arbitrary finite abelian group, and Hallgren's adaptation of Shor's algorithm to uncountable abelian groups—namely, to $\mathbb{R}$. Both pieces are essential ingredients in the quantum algorithm of Eisentr\"ager-Hallgren-Kitaev-Song to compute the unit group of a number field...
  • Shahed Sharif
    Mon May 8, 2017
    3:00 pm
    We will complete our discussion of Shor's algorithm for factoring integers. Then we will begin discussing Hallgren's quantum polynomial-time algorithm for solving Pell's equation x^2 - dy^2 = 1. The paper can be found at http://public.csusm.edu/ssharif/crypto/ Hallgren's idea is to adapt Shor's algorithm to estimate the...
  • Nathan Kaplan and Shahed Sharif
    Mon May 1, 2017
    3:00 pm
    The May 1 meeting will include Nathan continuing the topic from last time, and Shahed discussing the topic below. Suggestions for things to read before the seminar are also given below. Shahed's abstract: We will cover the basics of quantum computation, with the goal of understanding Shor's algorithm and, eventually, the Hidden Subgroup...
  • Nathan Kaplan
    Mon Apr 17, 2017
    3:00 pm
    Computing the Unit Group of a Number Field Starting from Pell’s equation and units in real quadratic fields, we will discuss the problem of computing the unit group of a number field. This will lead to a discussion of the Hidden Subgroup Problem, which arises in many quantum algorithms.  We will discuss recent work of Eisentrager,...