On Thursday, November 7, 2019 at 9:13:17 PM UTC+5:30, Subrata Nandi wrote:
>
> Thanks Emmanuel Charpentier for your reply. But the entry of my matrix is
> only symbolic variables. For example I am giving one short matrix.
>
R.<x0, x1, x2, x3, x4, x5, x6, x7, x8, x9>=Boolean PolynomialRing()
> 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]
>
> ]
>
This is a 10 x 10 matrix where each xi in GF(2). I need to find
(0,0,0,0,0,0,0,0,0,1)*y^(-1). This is a small example of what I need. In
actual case, n=512. Can you help me to find the inverse. Thanks in advance
man.
>
> 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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