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Samed Bajrić Laboratory for Open Systems and Networks, Jožef Stefan Institute, Ljubljana, Slovenia

\*Address all correspondence to: samed@e5.ijs.si

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Implementing Symmetric Cryptography Using Sequence of Semi-Bent Functions DOI: http://dx.doi.org/10.5772/intechopen.85023

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Author details

Laboratory for Open Systems and Networks, Jožef Stefan Institute, Ljubljana,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: samed@e5.ijs.si

Modern Cryptography – Current Challenges and Solutions

provided the original work is properly cited.

Samed Bajrić

Slovenia

14

Chapter 2

Abstract

1. Introduction

the strength of RSA.

also considered.

17

Anthony Overmars

Survey of RSA Vulnerabilities

provides the reader with an appreciation of the strength of RSA.

Keywords: survey, public keys, vulnerability

Rivest et al. patented (US) RSA. RSA forms the basis of most public encryption systems. It describes a public key encryption algorithm and certification process, which protects user data over networks. The patent expired in September 2000 and now is available for general use. According to Marketsandmarkets.com, the global network encryption market size is expected to grow from USD 2.9 billion in 2018 to USD 4.6 billion by 2023, at a compound annual growth rate (CAGR) of 9.8%. Major growth drivers for the market include increasing adoption of optical transmission, an increasing demand to meet various regulatory compliances and a growing focus on shielding organizations from network security breaches. In short, RSA forms the basis of almost all public encryption systems. This, however, is not without risk. This chapter explores some of these vulnerabilities in a mathematical context and

Rivest et al. patented (US) RSA, which forms the basis for most public encryption systems. RSA describes a public key encryption algorithm and certification process, which protects user data over networks. The patent expired in September 2000 and now is available for general use. According to Marketsandmarkets.com [1], the global network encryption market size is expected to grow from USD 2.9 billion in 2018 to USD 4.6 billion by 2023, at a compound annual growth rate (CAGR) of 9.8%. Major growth drivers for the market include increasing adoption of optical transmission, an increasing demand to meet various regulatory compliances and a growing focus on shielding organizations from network security breaches. In short, RSA forms the basis of almost all public encryption systems. This, however, is not without risk. This chapter explores some of these vulnerabilities in a mathematical context and provides the reader with an appreciation of

RSA is secure and difficult to factorize in polynomial time. Conventional sequential computing machines, running in polynomial time, take an unfeasible amount of CPU cycles to find factorization solutions to RSA keys. Quantum computing holds great promise; this, however, is realistically still some way off. Opportunities exist using conventional computing (sequential and parallel) using better mathematical techniques. A discussion on exploiting implementation flaws is

Of keen interest is our lack of understanding of prime numbers and their structure. The current perception is that there appears to be some underlying structure, but essentially, primes are randomly distributed. This is explored in Sections 8 and 12.

functions. In: Coding, Cryptography and Combinatorics. Basel: Birkahauser Verlag; 2004. pp. 3-28

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[20] Zhang W, Xiao G. Constructions of almost optimal resilient Boolean functions on large even number of variables. IEEE Transactions on Information Theory. 2009;55(12): 5822-5831

[21] Zhang W, Pasalic E. Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria. Information Sciences. 2017;376:21-30

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[25] Pasalic E, Gangopadhyay S, Zhang W, Bajric S. Design methods for semibent functions. Information Processing Letters. 2019:61-70
