(→Eve can decode the message without the Secret vector) |
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== Eve can decode the message without the secret matrix's inverse == | == Eve can decode the message without the secret matrix's inverse == | ||
| − | + | Eve knows 1 vector relates to the other by an unknown 3x3 matrix. If she breaks the large vectors into 3 smaller vectors and has taken linear algebra, she would hopefully recognize that the smaller vector are linearly independent and thus form an equivalent basis. All she has to do to uncover the any given message is rewrite the encrypted vector as a linear combination of the linearly independent encrypted vectors. Multiplying these coefficents by the decrypted vectors, she will intercept the message. | |
| + | |||
| + | == Decryption == | ||
| + | |||
| + | [2, 23, 3] is equal to: | ||
| + | |||
| + | 1[2 0 0] + 23[0 1 0] + 1[0 0 3] | ||
| + | |||
| + | using these coefficients: | ||
| + | |||
| + | 1[1 0 4] + 23[0 1 0] + 1[1 0 1] = [2 23 5] | ||
| + | |||
| + | Which stands for BWE. | ||
| + | |||
| + | another way to uncover the message is to rewrite the vectors she originally knew as 9 equation with 9 unknowns, and solve for the 9 unknowns to find the secret matrix. If she multiplies the encrypted code with the inverse of the secret matrix she will obtain her answer. | ||
| + | |||
| + | The Secret matrix is: | ||
| + | |||
| + | <math>\begin{bmatrix} | ||
| + | -2/3 & 0 & 4 \\ | ||
| + | 0 & 1 & 0 \\ | ||
| + | 2/3 & 0 & -1 | ||
| + | \end{bmatrix}</math> | ||
Latest revision as of 09:22, 18 September 2008
Bob can decode the message
All Bob has to do is invert the matrix and multiply the code with this inverted matrix 3 numbers at a time. Finally he can obtain the message by converting each number to it's corresponding alphabet character.
Eve can decode the message without the secret matrix's inverse
Eve knows 1 vector relates to the other by an unknown 3x3 matrix. If she breaks the large vectors into 3 smaller vectors and has taken linear algebra, she would hopefully recognize that the smaller vector are linearly independent and thus form an equivalent basis. All she has to do to uncover the any given message is rewrite the encrypted vector as a linear combination of the linearly independent encrypted vectors. Multiplying these coefficents by the decrypted vectors, she will intercept the message.
Decryption
[2, 23, 3] is equal to:
1[2 0 0] + 23[0 1 0] + 1[0 0 3]
using these coefficients:
1[1 0 4] + 23[0 1 0] + 1[1 0 1] = [2 23 5]
Which stands for BWE.
another way to uncover the message is to rewrite the vectors she originally knew as 9 equation with 9 unknowns, and solve for the 9 unknowns to find the secret matrix. If she multiplies the encrypted code with the inverse of the secret matrix she will obtain her answer.
The Secret matrix is:
$ \begin{bmatrix} -2/3 & 0 & 4 \\ 0 & 1 & 0 \\ 2/3 & 0 & -1 \end{bmatrix} $
