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Families of Pseudorandom Binary Sequences with Low Cross-Correlation Measure

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Cryptography and Information Security in the Balkans (BalkanCryptSec 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9024))

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Abstract

Pseudorandom sequences are used in many areas of cryptography for instance as a key stream of stream ciphers. These sequences have to be unpredictable and resist to known attacks, hence they are supposed to satisfy some properties e.g., large linear complexity and low correlation. Since they are generated by a sequence generator, we also need to talk about a family of sequences and its properties. A family of sequences must have complex and rich structure e.g., large family size, large family complexity, strict avalanche property and low cross-correlation. In this study, we present two large families of pseudorandom binary sequences with low cross-correlation measure. In fact, we extend the family construction method given by K. Gyarmati, C. Mauduit and A. Sárközy and obtain larger families.

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References

  1. Ahlswede, R., Khachatrian, L.H., Mauduit, C., Sárközy, A.: A complexity measure for families of binary sequences. Period. Math. Hungar. 46(2), 107–118 (2003)

    Article  MathSciNet  Google Scholar 

  2. Alon, N., Kohayakawa, Y., Mauduit, C., Moreira, C.G., Rödl, V.: Measures of pseudorandomness for finite sequences: typical values. Proc. Lon. Math. Soc. 95, 778–812 (2007)

    Article  Google Scholar 

  3. Cassaigne, J., Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences. VII. the measures of pseudorandomness. Acta Arith. 103(2), 97–118 (2002)

    Article  MathSciNet  Google Scholar 

  4. Goubin, L., Mauduit, C., Sárközy, A.: Construction of large families of pseudorandom binary sequences. J. Number Theory 106(1), 56–69 (2004)

    Article  MathSciNet  Google Scholar 

  5. Gyarmati, K.: On a family of pseudorandom binary sequences. Period. Math. Hungar. 49(2), 45–63 (2004)

    Article  MathSciNet  Google Scholar 

  6. Gyarmati, K., Mauduit, C., Sárközy, A.: The cross correlation measure for families of binary sequences. In: Applied Algebra and Number Theory, pp. 126–143. Cambridge University Press (2014)

    Google Scholar 

  7. Liu, H.: A family of pseudorandom binary sequences constructed by the multiplicative inverse. Acta Arith. 130(2), 167–180 (2007)

    Article  MathSciNet  Google Scholar 

  8. Mauduit, C., Sárközy, A.: On finite pseudorandom binary sequences. I. measure of pseudorandomness, the Legendre symbol. Acta Arith. 82(4), 365–377 (1997)

    MathSciNet  Google Scholar 

  9. NIST: Advanced encryption standard. Federal Information Processing Standard, FIPS-197 12 (2001)

    Google Scholar 

  10. Rivat, J., Sárközy, András: On pseudorandom sequences and their application. In: Ahlswede, Rudolf, Bäumer, Lars, Cai, Ning, Aydinian, Harout, Blinovsky, Vladimir, Deppe, Christian, Mashurian, Haik (eds.) General Theory of Information Transfer and Combinatorics. LNCS, vol. 4123, pp. 343–361. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Tóth, V.: Collision and avalanche effect in families of pseudorandom binary sequences. Period. Math. Hungar. 55(2), 185–196 (2007)

    Article  MathSciNet  Google Scholar 

  12. Winterhof, A., Yayla, O.: Family complexity and cross-correlation measure for families of binary sequences. The Ramanujan Journal online first (2014). doi:10.1007/s11139-014-9649-5

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Acknowledgment

This paper was written when the author was visiting Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz. The hospitality of RICAM is gratefully acknowledged. The author has benefited from discussions with Arne Winterhof. The visit was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Grant No. 2219. The author thanks anonymous referees for useful suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Hacettepe University, Beytepe Campus, Ankara, Turkey

    Oğuz Yayla

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  1. Oğuz Yayla
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Correspondence to Oğuz Yayla .

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Editors and Affiliations

  1. Istanbul Technical University, Istanbul, Turkey

    Berna Ors

  2. Katholieke Universiteit Leuven, Leuven, Belgium

    Bart Preneel

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Yayla, O. (2015). Families of Pseudorandom Binary Sequences with Low Cross-Correlation Measure. In: Ors, B., Preneel, B. (eds) Cryptography and Information Security in the Balkans. BalkanCryptSec 2014. Lecture Notes in Computer Science(), vol 9024. Springer, Cham. https://doi.org/10.1007/978-3-319-21356-9_3

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  • DOI: https://doi.org/10.1007/978-3-319-21356-9_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21355-2

  • Online ISBN: 978-3-319-21356-9

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