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? > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/1a4011b8-cc0e-4d89-a795-dcca54ef7f71%40googlegroups.com.