How to find linear complexity of non binary prime fields using berlekamp_massey algorithm in Sagemath?

Mathpdegeek497

4/12/24, 7:24 AM

I am having a prime field of large size (assume it of the type GF(2**18)) and I need to find linear complexity of a sequence (of some specified length) defined on this field. I am using the inbuilt berlekamp_massey function to get the linear complexity (the degree of minimal polynomial) of the sequence. Current Work:

from sage.matrix.berlekamp_massey import berlekamp_massey
F = GF(2**18)
.
.

#Function to get a primitive element
#function to generate the desired sequence
.
.
#sequence in hand Let's call it s
lin_complexity = berlekamp_massey(s).degree()
#The lin_complexity turns out to be a float which is incorrect

Issue I am getting wrong results as linear complexity is turning out to be a float number. Please help me understand how to calculate linear complexity of non-binary sequences in sagemath.

0 + 1

prime-numbers

lfsr

prime-field

fgrieu

4/12/24, 8:54 AM

But $\operatorname{GF}(2^{18})$ is not a prime field! Also, it is not of large size from a cryptographic standpoint. Perhaps show us what `type(s[0])`and `s[0].base_ring()` are. Does the problem happen with `s` shortened to `s[0:4]` ? Independently: this is more a Sagemath question than a crypto question.

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EN: How to find linear complexity of non binary prime fields using berlekamp_massey algorithm in Sagemath?

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