Enumeration of Correlation Immune Boolean Functions.

Date of Submission

December 2001

Date of Award

Winter 12-12-2002

Institute Name (Publisher)

Indian Statistical Institute

Document Type

Master's Dissertation

Degree Name

Master of Technology

Subject Name

Computer Science

Department

Applied Statistics Unit (ASU-Kolkata)

Supervisor

Maitra, Subhamoy (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

Correlation Immunity of boolean functions has long been recognized as one of the critical indicators. There are a lot of successful correlation attacks against a number of stream ciphers. To safeguard against such attacks it is necessary to develop boolean functions of high correlation immunity. In this paper I begin by looking at some definitions and derive some properties of correlation immune functions.The enumeration of correlation immune functions has also received wide attention. Though till date there is no perfect enumeration there are upper bounds, lower bounds and a lot of asymptotic results on the number of Correlation immune functions. I summarize few such results.At the end I discuss some properties of correlation immune functions f based on the hamming distance between f and though the results has been proved for 1st order correlation immune functions in [1], for higher order correlation immune functions I have observed the truth of those results for all correlation immune boolean functions with < 5 input variables, the results are yet to be proved.

Comments

ProQuest Collection ID: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:28843093

Control Number

ISI-DISS-2001-83

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

DOI

http://dspace.isical.ac.in:8080/jspui/handle/10263/6255

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