linear feedback shift register explained

I named 'xor' the output of the XOR function, not very correct. Here's the cleanest thing I could come up with after some lenghtier attempts (Python): def lfsr(seed, taps): To be more precise, that somehow showed how a LFSR works. So I wanted to write some small code for a program that worked like a LFSR. It took me some effort to understand, the final help was this really good page, much better than the (at first) cryptic wikipedia entry. Revisions and additional material are on the homepage of the book.Lately I bumped repeatedly into the concept of LFSR, that I find quite interesting because of its links with different fields and also fascinating in itself. Paper presented at the Eurocrypt ’86 (1986) Wang, M.Z., Massey, J.L.: The characterisation of all binary sequences with a perfect linear complexity profile. St Denis, T.: Cryptography for Developers. Shoup, V.: NTL: A library for doing number theory. Rueppel, R.A.: Analysis and Design of Stream Chiphers. Perron, O.: In: Die Lehre von den Kettenbrüchen. In: Advances in Cryptology-Eurocrypt ’89. Niederreiter, H.: Keystream sequncence with a good linear complexity profile for every starting point. (eds.) Advances in Cryptology, Eurocrypt ’87. Niederreiter, H.: Sequences with almost perfect linear complexity profile. Meidel, W., Niederreiter, H.: Linear complexity, k-error linear complexity, and the discrete Fourier transform. McGuire, G., Calerbank, A.R.: Proof of a conjecture of Sarwarte and Pursley regarding pairs of binary m-sequences. (ed.) Advances in Cryptology, Eurocrypt ’93. Matsui, M.: Linear cryptanalysis method for DES cipher. Massey, J.L.: Shift-register synthesis and BCH-decoding. Cambridge University Press, Cambridge (1986) Lidl, R., Niederreiter, H.: Introduction to Finite Fields and Their Applications. Technical Report R-285, Coordinated Science Laboratory, University of Illinois, Urbana, April 1966 Kasami, T.: Weight distribution formula for some class of cyclic codes. Kailath, T., Sayed, A.H.: Displacement structure: theory and applications. Helleseth, T., Kumar, P.V.: Sequences with low correlation. Graham, R.L., Knuth, D.E., Patashnik, O.: Concrete Mathematics, 2nd edn. Aegean Park, Laguna Hills, revised edition (1982) Golomb, S.W.: On the classification of balanced binary sequences of period 2 n−1. Gold, R.: Maximal recursive sequences with 3-valued cross-correlation functions. Theory 29, 600 (1983)ĭai, Z.d.: Proof of Rueppel’s linear complexity conjecture. Springer, New York (1995)Ĭheng, U., Golomb, S.W.: On the characterisation of PN sequences. (ed.) Advances in Cryptology EUROCRYPT 94. Academic Press, San Diego (1977)Ĭhabaud, F., Vaudenay, S.: Links between differential and linear cryptanalysis. 4(1), 3–72 (1991)Ĭasti, J.L.: Dynamical Systems and Their Applications: Linear Theory.

McGraw-Hill, New York (1968)īiham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. Springer, Berlin (1971)īerlekamp, E.R.: Algebraic Coding Theory.

Linear feedback shift register explained