Siegenthaler bound

Siegenthaler bound is a term in cryptology .

For the construction of a stream cipher in cryptography, a pseudo-random bit sequence is required, which is usually linked with the plain text XOR :

${\ displaystyle CT = PT \ oplus KS}$

In order for the cipher to be secure, the keystream should look like noise; H. the autocorrelation should be very low so that there is no correlation between the plain text and the ciphertext.

LFSR is usually used to produce this bit sequence . Normal LFSR are linear and thus generate a bit stream that can be recalculated relatively easily. For improvement, several LFSRs are combined with non-linear functions. Siegenthaler showed in 1984 that this worsened the correlation immunity of a sequence:

Let be a Boolean function with arguments and be correlations immune to the order , then the linear order of the function is limited upwards with: ${\ displaystyle f}$ ${\ displaystyle n}$ ${\ displaystyle f}$ ${\ displaystyle m}$

${\ displaystyle nm \ leq d}$

When implementing a stream cipher using non-linear combinations of LFSRs, a compromise must be made between the correlation immunity and the degree of linearity.

credentials

T. Siegenthaler: Correlation-Immunity of Nonlinear Combining Functions for Cryptographic Applications . In: IEEE Transactions on Information Theory . 30, No. 5, September 1984, pp. 776-780. doi : 10.1109 / TIT.1984.1056949 .

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