Definition
The linear complexity of a semi-infinite sequence \(\mathbf{s} = {({s}_{t})}_{t\geq 0}\) of elements of \({\mathbf{F}}_{q}\), \(\Lambda (\mathbf{s})\), is the smallest integer \(\Lambda \) such that \(\mathbf{s}\) can be generated by a linear feedback shift register (LFSR) of length \(\Lambda \) over \({\mathbf{F}}_{q}\), and is \(\infty \) if no such LFSR exists. By way of convention, the linear complexity of the all-zero sequence is equal to \(0\). The linear complexity of a linear recurring sequence corresponds to the degree of its minimal polynomial.
The linear complexity \(\Lambda (\mathbf{{s}^{n}})\) of a finite sequence \(\mathbf{{s}^{n}} = {s}_{0}{s}_{1}\ldots {s}_{n-1}\) of \(n\) elements of \({\mathbf{F}}_{q}\) is the length of the shortest LFSR which produces \(\mathbf{{s}^{n}}\) as its first \(n\)output terms...
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Rueppel RA (1986) Analysis and design of stream ciphers. Springer-Verlag, New York
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Canteaut, A. (2011). Linear Complexity. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_353
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DOI: https://doi.org/10.1007/978-1-4419-5906-5_353
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