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Structural proxies for black box rings encrypting rings of 2 by 2 matrices over finite fields of odd order

Alexandre Borovik, Sukru Yalcinkaya

Abstract

This paper provides an example of structural proxies for black box rings encrypting rings of 2 by 2 matrices of finite fields of odd order.

Structural proxies for black box rings encrypting rings of 2 by 2 matrices over finite fields of odd order

Abstract

This paper provides an example of structural proxies for black box rings encrypting rings of 2 by 2 matrices of finite fields of odd order.
Paper Structure (5 sections, 1 theorem, 36 equations)

This paper contains 5 sections, 1 theorem, 36 equations.

Table of Contents

  1. Introduction
  2. Black box algebra
  3. Axiomatic description of black box algebraic structures
  4. Structural proxy
  5. Proof of Theorem \ref{['th:m22']}

Key Result

Theorem 1

Let $\mathsf{R} \vDash {\rm M}_{2\times 2}(\mathbb{F})$ be a black box ring encrypting the ring of $2\times 2$ matrices over a finite field $\mathbb{F}$ of odd order. Assume that we know this order, $|\mathbb{F}| = q$. Then we can construct, in time polynomial in $\log q$, a black box field $\mathsf

Theorems & Definitions (1)

  • Theorem 1