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FRINATEK-Fri mat.,naturv.,tek

Secure Boolean Functions for Coding and Cryptography

Awarded: NOK 10.1 mill.

Boolean functions are functions that take several binary (i.e., {0,1}) variables and provide a binary output. Boolean functions are ubiquitous occurring at the heart of virtually all known digital system - computers, telecommunications and cryptographic primitives. The project found many new Boolean functions with applications in coding and cryptography. The results of the project have resulted in more than 60 publications in international leading refereed journals and conferences. The project has organized two international workshops on Boolean functions as well as the bi-annually international conference Workshop in Coding and Cryptography (WCC2013) that alternates between Bergen and Paris. The PhD student Chunlei Li in the project graduated in June 2014. His thesis contained many new results on Nonlinear Shift Register Sequences that could be analyzed using ideas from Boolean functions. He also used methods from Boolean functions to construct new optimal linear codes. The researcher Lilya Budaghyan completed her Habilitation degree in Paris 2013. She found new results on almost perfect nonlinear functions (APN) and classified bent Boolean functions using methods from geometry. She also received the Young Talents Research Award from NFR in 2014. The researcher Alexander Kholosha studied Boolean functions and cryptography. He found new results on bent functions and was invited to write a chapter on Bent Functions in the Handbook of Finite Fields that was published in 2013. The project leader Tor Helleseth worked on connections between Boolean functions, stream ciphers, sequences, and coding theory. He received a High-End Foreign-Expert Distinguished Visiting Professor Award from China to visit Soutwest Jiaotong University in Chengdu, China during the period 2012-2014. This resulted in excellent contacts and more than 25 publications with researchers from China. He was also appointed an honorary professor at the Hubei University in Wuhan.

Boolean functions are functions that take several binary (i.e., {0,1}) variables as input and provide a binary output. Boolean functions are ubiquitous, occurring at the heart of virtually all known digital systems - computers, telecommunications and cryp tographic primitives, for example, all depend on the theory of Boolean functions. There are many different Boolean functions even in very few variables so it is an important and very challenging task to find the best Boolean functions for each possible application. This project will focus on Boolean functions that have their main applications in coding theory and in particular in cryptography. These Boolean functions are important to improve the reliability and security of modern communication systems. The project will provide design and analysis of new and existing Boolean functions and make the results of the best Boolean functions available in a public website. The Selmer Center at the Department of Informatics at the UoB will lead the project. The project will collaborate with international researchers Claude Carlet, University of Paris 8, France, and Gregor Leander, DTU, Denmark. During the project period the project will: - Supervise one PhD student to complete his thesis on the classification and construction of highly nonlinear Boolean functions and maintain and update a database of the best functions. - Train a postdoctoral student to study links between APN and PN functions and other mathematical objects to provide new tools for solving pr oblems on APN and PN functions. - Hire one researcher who will work on and coordinate the investigations proposed by this project. - Invite leading international researchers for visits, advanced guest lectures, workshops and research on secure Boolean fun ctions. - Publish at least 20 papers in leading international journals and conferences

Funding scheme:

FRINATEK-Fri mat.,naturv.,tek