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Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation

Ren, Ai
http://orcid.org/0000-0002-8315-6902
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262

Abstract Details

2019, PhD, University of Cincinnati, Arts and Sciences: Mathematical Sciences.
In 2011, Gao and Heindl proposed a family of Multivariate Public Key Cryptosystems by combining the triangular scheme and the oil-vinegar scheme. The new design was claimed to be secured under known attacks. Besides that, they also used the Medium-Field Multivariate Public Key Cryptosystem as an example of their general frame and explained how it works. Later, by introducing several Diophantine equations into their design, they presented the Diophantine Equations Multivariate Public Key Cryptosystem (DEMPKC) with three sets of suggested parameters and the claimed security level were high. In this paper, we present our cryptanalysis on DEMPKC. Our cryptanalysis uses embedded surfaces associated with the DEMPKC and shows the attack can break the system efficiently. Our work provides an example of more general embedded surfaces other than linearization type of equations can be very useful to attack cryptosystems.
Jintai Ding, Ph.D. (Committee Chair)
Seungki| Kim, Ph.D. (Committee Member)
Benjamin Vaughan, Ph.D. (Committee Member)
172 p.
Mathematics
Multivariate Public Key Cryptosystem; Cryptosystem; Diophantine equations; embedded surface attach; linearization type of equation; cryptography

Recommended Citations

Citations

  • Ren, A. (2019). Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262

    APA Style (7th edition)

  • Ren, Ai. Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation. 2019. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262.

    MLA Style (8th edition)

  • Ren, Ai. "Embedded Surface Attack on Multivariate Public Key Cryptosystems from Diophantine Equation." Doctoral dissertation, University of Cincinnati, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1558364211159262

    Chicago Manual of Style (17th edition)

ucin1558364211159262
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This open access ETD is published by University of Cincinnati and OhioLINK.