Mathematical Research Seminar - Archive
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This talk will cover certain applications of Boolean functions in cryptography and related research fields in this context. I will briefly mention the main research directions conducted by the staff at Centre of Cryptology at UP FAMNIT that include minimal linear codes, search for (more) perfect combinatorial objects, post-quantum cryptology and cryptanalysis. Future perspectives and development of Centre of Cryptology will also be briefly mentioned.
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In early nineties C.Carlet introduced two new classes of bent functions, both derived from the Maiorana-McFarland (MM) class, and named them C and D class, respectively. Apart from a subclass of D and C, denoted by $D_0$ by Carlet, which is provably outside two main (completed) primary classes of bent functions, little is known about their efficient constructions. In this talk, I will give an overview of some known results, and present some new results, related to the bent functions in the C class, provably outside the completed MM class.
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Linear codes have been widely used in communication systems since the beginning of the digital age. Mathematical research focused on error-correcting codes because of their important applications in data transmission. However, a special type of linear codes, called minimal, has proven to be useful for defining access structures in secret sharing schemes and secure two-party computation. This motivated research in this field.
Minimal codes can be constructed using a simple condition first proposed by Ashikhmin and Barg in 1998. Until the groundbreaking work of Ding, Heng and Zhou in 2018 there were no known examples of infinite families of minimal codes that violated this condition. Since then, several examples of such families have been constructed.
In this talk we present three generic constructions of families of minimal codes that violate Ashikhmin and Barg's condition based on characteristic functions of suitable sets. This is a joint work with E. Pasalic, F. Zhang and Y. Wei.
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In the first part of the talk, we give basic definitions and properties of some cryptographically significant mappings, including (vectorial) bent functions, s-plateaued function, APN and AB functions as well as the notion of duals of bent and s-plateaued functions.
In the second part of the talk (joint work with Enes Pasalic and Samir Hodžić) we present some results and current research topics: Characterization of semi-bentness (bentness) of the component functions (duals of component functions) of the Gold AB function in spectral domain; Generic construction of vectorial bent functions motivated by the constructions of Zheng et al. (construction of vectorial bent functions) and Tang et al. (construction of bent functions).
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This is the first in a series of seminars by members of the Center of Cryptography. Our research has many practical applications, and in the first lecture we will look at what motivates the development of post-quantum cryptography. Quantum computers are still a myth of some distant future for many, but in reality, standardisation of cryptographic algorithms that will be resistant to quantum attacks is already underway. It is expected that the migration to new algorithms will be a difficult and long process. But what will the first working quantum computer mean for our digital world? And how many currently implemented security algorithms will be broken?
Let us recall you that, due to the new measures at UP FAMNIT premises regarding the prevention of the spread of coronavirus, lectures at our Math Research Seminar will only be broadcasted via Zoom.
We are looking forward to meet at the video-conference throughout the following link:
Join Zoom Meeting HERE!
For more info visit our YouTube Channel.
