Abstract
In cryptography, the property of randomness in pseudo-random generators is very important to avoid any pattern in output sequences, to provide security against attacks, privacy and anonymity. In this article, the randomness of the family of sequences obtained from the generalized self-shrinking generator is analyzed. Moreover, the characteristics, generalities and relationship between the t-modified self-shrinking generator and the generalized self-shrinking generator are presented. We find that the t-modified self-shrunken sequences can be generated from a generalized self-shrinking generator. Then, an in-depth analysis of randomness focused on the generalized sequences by means of complete and powerful batteries of statistical tests and graphical tools is done, providing a useful vision of the behaviour of these sequences and proving that they are suitable to be used in cryptography.
Highlights
In cryptography, randomness plays an important role in multiple and diverse applications.Random numbers are employed to generate cryptographic keys, challenges, nonces, to encrypt messages and at different steps of cryptographic algorithms and protocols [1,2,3,4].A pseudo-random number generator is an algorithm for creating a sequence of numbers that is supposed to be indistinguishable from a uniformly chosen random sequence
In cryptography, where the security of many cryptographic schemes lies in the quality of pseudorandom generators, it is necessary that the sequences meet the following requirements—(1) the generated sequence must not be distinguished from a truly random sequence; (2) the sequence must be unpredictable; (3) the sequence period must be very large; (4) the key space must be large enough for a brute or exhaustive force attack to be impossible; (5) the design of the generator should be resistant to the specialized attacks reported in the literature
We have found a relationship between two families of binary sequences belong to the class of decimation-based sequence generators, that is, the t-modified self-shrunken sequences can be generated from a generalized self-shrinking generator
Summary
Randomness plays an important role in multiple and diverse applications. There is no mathematical proof that ensures the randomness of a bit sequence; there exists a huge number of empirical tests to determine if a sequence is random enough and secure to be used in cryptography [5]. If the sequences of a generator pass the statistical tests, this could be accepted as a generator of random sequences. The randomness of these sequences has never been analysed with such a complete battery of tests. The randomness of the family of sequences obtained from the generalized self-shrinking generator is analyzed. An in-depth analysis of randomness focused on the generalized sequences by means of complete batteries of statistical tests was done.
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