Part 1

Bob can decrypt the message by using the inverse of the secret matrix. Multiplying the encrypted vector three at a time by the inverse matrix will yield the original vector.

Part 2

Eve can decrypt the message without finding the secret matrix because the system in linear. The three vectors of the encrypted vector form a basis for all vectors because they are linearly independent. In other words, [encrypted vector]$ =a[2,0,0] + b[0,1,0] + c[0,0,3] $ where a,b,c are real numbers.

Part 3

Applying the method from part 2, we know that: $ [2,23,3]=a[2,0,0] + b[0,1,0] + c[0,0,3] $ so

$ 2=2a $, $ 23=1b $, and $ 3=3c $. therefore, a=1, b=23, and c=1.

Now apply the same coefficients to the known message that yielded the encrypted basis, [1,0,4,0,1,0,1,0,1].

$ 1[1,0,4] + 23[0,1,0] + 1[1,0,1]=[1+1,23,4+1]=[2,23,5] $

[2,23,5] corresponds to BWE.

The other way of doing this is to set up equations to find the 3 x 3 matrix. however, There is a greater chance of making a mistake.

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Sees the importance of signal filtering in medical imaging

Dhruv Lamba, BSEE2010