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# Accession Number:

## ADA561969

# Title:

## Computing the Algebraic Immunity of Boolean Functions on the SRC-6 Reconfigurable Computer

# Descriptive Note:

## Master's thesis

# Corporate Author:

## NAVAL POSTGRADUATE SCHOOL MONTEREY CA

# Report Date:

## 2012-03-01

# Pagination or Media Count:

##
172.0

# Abstract:

## Boolean functions with high algebraic immunity AI are vital in reducing the possibility of utilizing algebraic attacks to break an encryption system. Simple algorithms exist to compute the AI of a given n-variable Boolean function, but the time required to test a large number of functions is much greater on conventional computing systems. AI was computed for all functions through n 5 using the SRC-6. AI was also computed for n 5 using a C algorithm. The SRC-6 performed 4.86 times faster than a conventional processor for this computation. It is believed that this is the first enumeration of all 5-variable functions with respect to AI. Monte Carlo trials were performed for n 6, both on the SRC-6 and utilizing a C algorithm on a conventional processor. These trials provided the first known distribution of AI for 6-variable functions. Some algorithms for computing AI require a conversion between the truth table form of the function and its algebraic normal form. The first known Verilog implementation of a reduced transeunt triangle was developed for this conversion. This reduced form requires many fewer gates and has On delay versus O2 n delay for a full transeunt triangle.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#