Computing Algebraic Immunity by Reconfigurable Computer

Abstract

Algebraic immunity (AI) is a property of a Boolean function f that measures its susceptibility to an algebraic attack. If f has a low algebraic immunity and f is used in an encryption protocol, then there are ways to successfully cryptanalyze the system. As a result, it is important to have an efficient means to compute the algebraic immunity of Boolean functions. Unfortunately, algebraic immunity is one of the most complex cryptographic properties to compute. For example, it is significantly more difficult to compute than nonlinearity [2]. Here, we show the advantage of a reconfigurable computer in computing a function's algebraic immunity. For example, we show that a reconfigurable computer is 4.9 times faster than a conventional computer in this computation for 5-variable functions. Indeed, we compute the distribution of functions to algebraic immunity for all 5-variable functions, a computation that has not been previously accomplished. Interestingly, the problem we address is to design a logic circuit that computes a characteristic of a logic function.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 2012
Accession Number
ADA613768

Entities

People

  • Jon T. Butler
  • M. E. Mccay
  • Pantelimon Stanica

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Advanced Electronics
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Applied Mathematics
  • Computations
  • Computers
  • Computing Devices
  • Equations
  • Frequency
  • Functions (Mathematics)
  • Immunity
  • Information Operations
  • Linear Algebra
  • Linear Systems
  • Mathematical Analysis
  • Mathematics
  • Monte Carlo Method
  • Simultaneous Equations
  • Vector Spaces

Fields of Study

  • Computer science
  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computer Networking
  • Optical Fiber Sensing and Electromagnetic Propagation.