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I need to find inverse of 4*4 byte binary matrix , when i searched i found some algorithm can be used to solve this problem but i don't know how to implement it . the algorithm is named " the extended Euclid algorithm"?
a 4 x 4 matrix of integers in [-128, 127] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
a 4 x 4 matrix of integers in [0, 255] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
This is because some elements do not have inverses themselves. for example 1 = (2 * x) mod 256 has no solution if x must be an integer.
a 32 x 32 matrix of {0,1} where "+" is "xor" and "*" is "and"? This could have an inverse.
a 4 x 4 matrix of elements of a gf256? This could have an inverse.
These don't have numeric interpretations.
a 4 x 4 matrix of integers in [-128, 127] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
a 4 x 4 matrix of integers in [0, 255] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
This is because some elements do not have inverses themselves. for example 1 = (2 * x) mod 256 has no solution if x must be an integer.
a 32 x 32 matrix of {0,1} where "+" is "xor" and "*" is "and"? This could have an inverse.
a 4 x 4 matrix of elements of a gf256? This could have an inverse.
These don't have numeric interpretations.
What part are you having trouble with? You may be having problems as 8b values can have 256 values, but 256 is not a prime number. As a result, not all bytes have a modular inverse.
What part are you having trouble with? You may be having problems as 8b values can have 256 values, but 256 is not a prime number. As a result, not all bytes have a modular inverse.
If the binary values represent numbers, and addition/multiplication are done in the normal way, then you can't always solve for the inverse. 1 = (2*x) % 256 has no solution in integers -- even numbers don't have a multiplicative inverse. Thus [2,0,0;0,2,0;0,0,2] has no solution.
If the binary values represent numbers modulo a prime (eg, mod 251), and addition/multiplication are done modulo that prime, then you can invert any invertable matrix. however, 251, 252, 253, 254, and 255 are no longer valid values. Also addition/multiplication are done modulo 251, which can be annoying.
If the binary values represent non-numbers from a galois field, then you can invert any invertable matrix. However, addition and multiplication are weird and the binary values don't represent numbers.
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