PLEASE SHOW FULL DETAILED STEP BY STEP WORK Cryptography is the study of making

Question

PLEASE SHOW FULL DETAILED STEP BY STEP WORK

Cryptography is the study of making and using secret codes (see section 8.14). A text message is encoded using some mechanism and then wnt to a receiver. The receiver knows what mechanism the sender used to encode the mrautge and hence knows how to decode the message. Anyone else intercepting the message will be unable to read it. Suppose that the message is the phrase "LEAVE NOW". The first step is to convert the letters to numbers using some numbering scheme like: Then the message becomes: LEAVE MOWrightarrow [12. 5, 1, 22, 5, 0, 14, 15, 23] A matrix with integer entries whose inverse also has integer entries can be used to encode and decode messages as follows. Suppose the matrix and its inverse are A = [-1 0 -1 2 3 4 2 4 5] A^1 = [1 4 -3 2 3 -2 -2 -4 3] We can represent our message as a 3 by 3 matrix (read down the columns): M = [L V N E E O A W] [12 22 14 5 5 15 1 0 23] The encoded message is E = AM. E =[-1 0 -1 2 3 4 2 4 5][12 22 14 5 5 15 1 0 23] = [-13 -22 -37 43 59 165 49 64 203] The encoded message can only be decoded if we know the matrix A used to encode it. The encoded message E can be decoded simply by multiplying it by A^-1. That is: M = A^-1 E = [1 4 -3 2 3 -2 -2 -4 3][-13 -22 -37 43 59 165 49 64 203] = [12 22 14 5 5 15 1 0 23] [L V N E E O A W] Decode the message: E = [-169 -67 -104 46 17 17 171 67 120] Where the message was encoded using the matrix: A = [-3 -3 -4 0 1 1 4 3 4]

Explanation / Answer

First determine A-1 =

Determine the message matrix M by

M = A-1 E=

which translates to

BUY APPLE

1 0 1 4 4 3 -4 -3 -3

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.