Gaussian elimination in split unitary groups with an application to public-key cryptography

In this chapter, we study the MOR cryptosystem with symplectic and orthogonal groups over finite fields of odd characteristics. There are four infinite families of finite classical Chevalley groups. These are special linear groups SL(d, q), orthogonal groups O(d, q), and symplectic groups Sp(d, q). The family O(d, q) splits into two different families of Chevalley groups depending on the parity of d. The MOR cryptosystem over SL(d, q) was studied by the second author. In that case, the hardness of the MOR cryptosystem was found to be equivalent to the discrete logarithm problem in F q d . In this chapter, we show that the MOR cryptosystem over Sp(d, q) has the security of the discrete logarithm problem in F q d . However, it seems likely that the security of the MOR cryptosystem for the family of orthogonal groups is F q d 2 . We also develop an analog of row-column operations in symplectic and orthogonal groups which is of independent interest as an appendix.

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“…The cryptosystem that we have in mind is the MOR cryptosystem [6][7][8][9]. In Section 2, we describe the MOR cryptosystem in details.…”

Section: Introductionmentioning

confidence: 99%

The MOR Cryptosystem in Classical Groups with a Gaussian Elimination Algorithm for Symplectic and Orthogonal Groups

Bhunia¹,

Mahalanobis²,

Shinde³

et al. 2019

Modern Cryptography - Theory, Technology, Adaptation and Integration [Working Title]

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“…We call our algorithms Gaussian elimination in symplectic and orthogonal groups respectively. Similar algorithm for unitary groups [13] is available.…”

Section: Introductionmentioning

confidence: 99%