Thanks Emmanuel Charpentier for your reply. But the entry of my matrix is
only symbolic variables. For example I am giving one short matrix.
y=[
[x0 x1 x2 x3 x4 x5
x6 x7 x8 x9]
[x1 x2 x3 x4 x5 x6
x7 x8 x9 x0 + x3]
[x2 x3 x4 x5 x6 x7
x8 x9 x0 + x3 x1 + x4]
[x3 x4 x5 x6 x7 x8
x9 x0 + x3 x1 + x4 x2 + x5]
[ x4 x5 x6 x7 x8 x9
x0 + x3 x1 + x4 x2 + x5 x3 + x6]
[ x5 x6 x7 x8 x9 x0 + x3
x1 + x4 x2 + x5 x3 + x6 x4 + x7]
[ x6 x7 x8 x9 x0 + x3 x1 + x4
x2 + x5 x3 + x6 x4 + x7 x5 + x8]
[ x7 x8 x9 x0 + x3 x1 + x4 x2 + x5
x3 + x6 x4 + x7 x5 + x8 x6 + x9]
[ x8 x9 x0 + x3 x1 + x4 x2 + x5 x3 + x6
x4 + x7 x5 + x8 x6 + x9 x0 + x3 + x7]
[ x9 x0 + x3 x1 + x4 x2 + x5 x3 + x6 x4 + x7
x5 + x8 x6 + x9 x0 + x3 + x7 x1 + x4 + x8]
]
On Monday, November 4, 2019 at 12:20:50 AM UTC+5:30, Emmanuel Charpentier
wrote:
>
> One can check that Sage's built-in methods can invert such a GF(2) maytrix
> in reasonable time:
>
> sage: MS=MatrixSpace(GF(2),512,512)
> sage: while True:
> ....: M=MS.an_element()
> ....: if M.is_unit(): break
> ....:
> sage: %time IM=M^-1
> CPU times: user 2.99 ms, sys: 243 µs, total: 3.23 ms
> Wall time: 113 ms
> sage: bool(IM*M==diagonal_matrix(GF(2),[GF(2)(1)]*512))
> True
>
> But, being totally ignorant of your domain, I have trouble seeing how to
> use this result for boolean logic. A glimpse at the relevant documentation
> <http://doc.sagemath.org/html/en/reference/logic/index.html> hints that I
> should refrain from commenting further...
>
> HTH, nevertheless,
>
>
> Le jeudi 31 octobre 2019 10:51:27 UTC+1, Subrata Nandi a écrit :
>>
>> My research area is symmetric key cryptology. I need an efficient
>> algorithm for solving inverse of symbolic matrix of size 512 x 512 in
>> GF(2). Can anyone share
>> Idea regarding that?
>
>
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