THE IMUNAL EXECUTABLE FOR USERS

NAME

imunal - a program that computes the algebraic immunity of boolean functions

SYNOPSIS

imunal [ --version | ... [-v | -q | FILE | -majority n] ... ]

DESCRIPTION

Imunal is a program that computes the algebraic immunity (AI) of boolean functions. The boolean function whose AI is to computed must be given of the following form.

M0 + M1 + M2 + ... + Mn

Each Mi is either 1 or a form where the variables must be x1, x2... All the variables within a form must not be separated by any character. For example x1x2x3 is a valid form whereas x1 x2x3 and x1x2 x3 are not valid forms. A valid boolean function is given as an example below.

1 + x1x2 + x2x3 + x3x4 + x4x5

Note that between forms, spaces, line feeds, tabs, '+' characters can be put. As an example the form from the example above can be written

1
+ x1x2
+ x2x3
+ x3x4
+ x4x5

The number of variables of a boolean functions is determined as the maximum variable number encountered in a boolean function. Note that this has no consequences on the AI.

Boolean functions are contained in FILE. One or more files can be specified in which case the AI of each boolean function in each file will be computed and printed to standard output. If FILE is - the boolean function is read from standard input. If no file is given the boolean function is also read from standard input.

OPTIONS

--version

Print the version of imunal.

-v

Print some extra informations before the AIs of the boolean functions that follows on the command line. The output of imunal will be of the form

FILE: t1, t2, AI

where t1 indicates the time in seconds taken to compute the fiber over 1, t2 indicates the time in seconds taken to compute the AI, and AI is the AI.

-q

Quiet imunal. This option is useful to disable a previous -v option. This is the default behavior of imunal. The output of imunal will then be of the form

FILE: AI

where AI is the AI.

-majority n

Compute the AI of the majority function in n variables. Note that majority functions are optimal functions. The AI of this function in n variables is ceil(n / 2). Note that imunal actually computes the AI as if it was not known. This family of functions can be used to test imunal.

AUTHOR

Imunal and this man page were written by Guillaume Quintin <quintin@lix.polytechnique.fr>.