By Natalia Tokareva
Bent services: effects and functions to Cryptography
offers a different survey of the gadgets of discrete arithmetic often called Boolean bent capabilities. As those maximal, nonlinear Boolean features and their generalizations have many theoretical and useful purposes in combinatorics, coding conception, and cryptography, the textual content presents a close survey in their major effects, proposing a scientific evaluate in their generalizations and purposes, and contemplating open difficulties in type and systematization of bent features.
The textual content is suitable for beginners and complicated researchers, discussing proofs of numerous effects, together with the automorphism team of bent features, the reduce certain for the variety of bent features, and more.
- Provides a close survey of bent features and their major effects, featuring a scientific review in their generalizations and applications
- Presents a scientific and certain survey of countless numbers of ends up in the world of hugely nonlinear Boolean features in cryptography
- Appropriate assurance for college kids from complicated experts in cryptography, arithmetic, and creators of ciphers
Read or Download Bent Functions: Results and Applications to Cryptography PDF
Similar cryptography books
A result of quick development of electronic communique and digital facts trade, details safety has turn into a vital factor in undefined, enterprise, and management. sleek cryptography offers crucial innovations for securing info and keeping info. within the first half, this booklet covers the main ideas of cryptography on an undergraduate point, from encryption and electronic signatures to cryptographic protocols.
This ebook constitutes the refereed complaints of the seventh overseas Workshop on thought and perform in Public Key Cryptography, PKC 2004, held in Singapore in March 2004. The 32 revised complete papers offered have been rigorously reviewed and chosen from 106 submissions. All present concerns in public key cryptography are addressed starting from theoretical and mathematical foundations to a huge number of public key cryptosystems.
This e-book makes a truly obtainable advent to an important modern program of quantity idea, summary algebra, and chance. It comprises quite a few computational examples all through, giving newbies the chance to use, perform, and payment their knowing of key ideas. KEY subject matters insurance begins from scratch in treating chance, entropy, compression, Shannon¿s theorems, cyclic redundancy assessments, and error-correction.
- Public Key Cryptography: Applications and Attacks
- Privacy, Security and Trust within the Context of Pervasive Computing (The Springer International Series in Engineering and Computer Science)
- Noiseless Steganography: The Key to Covert Communications
- Expert SQL Server 2008 Encryption (Expert's Voice in SQL Server)
Additional resources for Bent Functions: Results and Applications to Cryptography
It is easy to see that there are bent functions of all other possible degrees from 2 to n/2 if n 4 (just use the Maiorana-McFarland construction for this; see Theorem 34). For example, the quadratic Boolean function f (x1 , . . , xn ) = x1 x2 ⊕ x3 x4 ⊕ · · · ⊕ xn−1 xn is bent for any even n. Note that in 2004 Hou  determined the bound for p-ary bent functions—namely, he proved that if f is a p-ary bent function (p is prime) (p−1)n + 1. In addition, if f is weakly regular, in n variables, then deg(f ) 2 (p−1)n then deg(f ) 2 .
If n is odd, then everything is completely different. First, the exact upper bound for nonlinearity of a Boolean function in n variables is still unknown! This question is as attractive as it is complicated. Some results on it can be found in articles by Maitra and Sarkar  and Kavut et al. , among others. Bent Functions: An Introduction 21 A Boolean function is called maximal nonlinear if its nonlinearity is as big as possible. Recall that if n is even, such a definition coincides with the definition of a bent function.
In 1993, Matsui  showed that DES is not resistant to linear cryptanalysis. For almost 20 years (from 1980 to 1998), DES was a standard of symmetric encryption in the USA. The weakness of the cipher consisted in the “bad” cryptographic properties of its nonlinear components—S-boxes. Mathematically, an S-box is a vectorial Boolean function that maps n input bits to m output bits. In DES, there are eight distinct S-boxes, completely defined in the standard (they can be easily found, for example, on the Internet).