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Growth of the ideal generated by a quadratic multivariate function

Kruglov, Victoria
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282931168

Abstract Details

2010, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
We find exact formulas for the growth of the ideal λAk, where λ is a quadratic element of the algebra of functions over the Galois field 𝔽q for q = 2 and q = 3. More precisely, we calculate dim(λAk), where Ak is the subspace of elements of degree less than or equal to k. The results clarify some of the assertions made in the articles of Yang, Chen, and Courtois [YC], [YCC] regarding the complexity of the XL algorithm.
Jintai Ding, PhD (Committee Chair)
Timothy Hodges, PhD (Committee Member)
Dieter Schmidt, PhD (Committee Member)
94 p.
Mathematics
multivariate; quadratic; XL algorithm; complexity; homology; semi-regular

Recommended Citations

Citations

  • Kruglov, V. (2010). Growth of the ideal generated by a quadratic multivariate function [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282931168

    APA Style (7th edition)

  • Kruglov, Victoria. Growth of the ideal generated by a quadratic multivariate function. 2010. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282931168.

    MLA Style (8th edition)

  • Kruglov, Victoria. "Growth of the ideal generated by a quadratic multivariate function." Doctoral dissertation, University of Cincinnati, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1282931168

    Chicago Manual of Style (17th edition)

ucin1282931168
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This open access ETD is published by University of Cincinnati and OhioLINK.