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Even without knowledge of the secret matrix, it is possible to decrypt the message by applying the principles of linearity. Eve can write any encrypted message that she receives as a linear combination of the one encrypted message of which she has knowledge. In other words the encrypted message (2,0,0,0,1,0,0,0,3) that Eve has intercepted can be broken down into the 3 vectors <2,0,0>, <0,1,0>, and <0,0,3>. These vectors form a basis, which allows other vectors to be written in terms of this basis. For example, the vector <4,5,9> can be written as <2,5,3> as follows: | Even without knowledge of the secret matrix, it is possible to decrypt the message by applying the principles of linearity. Eve can write any encrypted message that she receives as a linear combination of the one encrypted message of which she has knowledge. In other words the encrypted message (2,0,0,0,1,0,0,0,3) that Eve has intercepted can be broken down into the 3 vectors <2,0,0>, <0,1,0>, and <0,0,3>. These vectors form a basis, which allows other vectors to be written in terms of this basis. For example, the vector <4,5,9> can be written as <2,5,3> as follows: | ||
| − | '''<math>2</math>'''<math>\cdot | + | '''<math>2</math>'''<math>\cdot (2,0,0) \; + \;</math>'''<math>5</math>'''<math><2,0,0> \; + \;</math> |
==Decryption of (2,23,3)== | ==Decryption of (2,23,3)== | ||
Revision as of 18:12, 17 September 2008
Decrypting the Message w/ Knowledge of the Secret Matrix
Bob can decrypt the message simply by finding the inverse of the secret matrix and multiplying each set of 3 values in the encrypted vector by the inverse matrix to get back the original message vector.
Decrypting the Message w/o Knowledge of the Secret Matrix
Even without knowledge of the secret matrix, it is possible to decrypt the message by applying the principles of linearity. Eve can write any encrypted message that she receives as a linear combination of the one encrypted message of which she has knowledge. In other words the encrypted message (2,0,0,0,1,0,0,0,3) that Eve has intercepted can be broken down into the 3 vectors <2,0,0>, <0,1,0>, and <0,0,3>. These vectors form a basis, which allows other vectors to be written in terms of this basis. For example, the vector <4,5,9> can be written as <2,5,3> as follows:
$ 2 $$ \cdot (2,0,0) \; + \; $$ 5 $$ <2,0,0> \; + \; $
