Abstract
This paper presents intermediate results of our investigations into the potential of analog hardware for the purpose of solving linear equation (LES) systems which are of quadratic form and binary. Based on the assumption that we can efficiently solve binary LES over the rationals with sufficient precision, we present a generic method to map a rational solution to a solution which solves the equation system over \(\mathbb{F}_2\). We show that, in order to perform this mapping, we only need to look at two bits of the binary expansion of each of the elements of the rational solution vector.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barkan, E., Biham, E., Keller, N.: Instant Ciphertext-Only Cryptanalysis of GSM Encrypted Communication. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 600–616. Springer, Heidelberg (2003)
Gendrullis, T., Novotný, M., Rupp, A.: A Real-World Attack Breaking A5/1 within Hours. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 266–282. Springer, Heidelberg (2008)
Golić, J.D.: Cryptanalysis of Alleged A5 Stream Cipher. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 239–255. Springer, Heidelberg (1997)
Lenstra, A., Lenstra, H., Manasse, M., Pollard, J.: The number field sieve. In: The Development of the Number Field Sieve, pp. 11–42 (1993)
Lenstra, A.K., Shamir, A.: Analysis and Optimization of the TWINKLE Factoring Device. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 35–52. Springer, Heidelberg (2000)
Petrovic, S., Fuster-Sabater, A.: Cryptanalysis of the A5/2 Algorithm. Technical report (2000), http://eprint.iacr.org/
Pornin, T., Stern, J.: Software-Hardware Trade-Offs: Application to A5/1 Cryptanalysis. In: Paar, C., Koç, Ç.K. (eds.) CHES 2000. LNCS, vol. 1965, pp. 318–327. Springer, Heidelberg (2000)
Shamir, A.: Factoring Large Numbers with the TWINKLE Device (Extended Abstract). In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 2–12. Springer, Heidelberg (1999)
Shamir, A., Tromer, E.: Factoring Large Numbers with the TWIRL Device. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 1–26. Springer, Heidelberg (2003)
Yeung, T., Poon, E.: Binary decimal numbers and decimal numbers other than base ten. In: Proceedings of the International Conference on The Future of Mathematics Education (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Driessen, B., Paar, C. (2012). Solving Binary Linear Equation Systems over the Rationals and Binaries. In: Özbudak, F., RodrÃguez-HenrÃquez, F. (eds) Arithmetic of Finite Fields. WAIFI 2012. Lecture Notes in Computer Science, vol 7369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31662-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-31662-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31661-6
Online ISBN: 978-3-642-31662-3
eBook Packages: Computer ScienceComputer Science (R0)