An Application of Hadamard Transform to Test Stream Ciphers
In this chapter, we discuss results obtained on an application of the Hadamard transform to cryptanalysis, and in particular, we determine the probability to decipher different pseudo-random number generators used as components of stream ciphers.
- PDF / 258,135 Bytes
- 8 Pages / 439.36 x 666.15 pts Page_size
- 48 Downloads / 208 Views
An Application of Hadamard Transform to Test Stream Ciphers Guillermo Sosa-Gómez
, Omar Rojas
, and Octavio Páez-Osuna
Contents 19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.2 Hadamard Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.3 Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
255 256 256 259 262 262
19.1 Introduction When designing stream ciphers, a number of properties must be taken into account besides generating randomly looking bit sequences [4]; the generated sequence must present the most unpredictable behavior possible, that is, given a fraction of the sequence, it should not be possible to predict the rest, either before or after the given subsequence. In this chapter, we develop theoretical statistical attacks by searching for autocorrelations in the output bits of stream ciphers. The term cryptanalysis is also used to refer to any attempt to circumvent the security of different types of algorithms and cryptographic protocols in general, and not just encryption [7]. Although the objective has always been the same, i.e., totally breaking the cryptosystem, the methods and techniques of cryptanalysis have changed drastically throughout the history of cryptography, adapting to a growing cryptographic complexity, which
G. Sosa-Gómez () · O. Rojas Universidad Panamericana, Escuela de Ciencias Económicas y Empresariales, Zapopan, Jalisco, México e-mail: [email protected]; [email protected] O. Páez-Osuna Ronin Institute for Independent Scholarship, Montclair, NJ, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 P. Vasant et al. (eds.), Data Analysis and Optimization for Engineering and Computing Problems, EAI/Springer Innovations in Communication and Computing, https://doi.org/10.1007/978-3-030-48149-0_19
255
256
G. Sosa-Gómez et al.
ranges from the pen and paper methods of the past, through machines like Enigma to the systems based on modern computers and other electronic devices. To overcome the complexities of modern-day cryptography, we must resort to advanced mathematics and algorithms. A very useful mathematical technique to reduce the complexity of a
