9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m-20 a - 5e -m+24 -a +6e and two possible encryption keys =(1-3). E₁ = t-5v -t+6v h-5a -h+6a 4 2 16 3-21 E₂-8 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.
9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an encryption matrix E. The encrypted message will be the product of those two matrices, i.e. A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting the message requires performing the reverse operation to retrieve M from A. You have been sent an encrypted message: A = m-20 a - 5e -m+24 -a +6e and two possible encryption keys =(1-3). E₁ = t-5v -t+6v h-5a -h+6a 4 2 16 3-21 E₂-8 (a) Without performing any calculation, determine which of the encryption keys was used to encrypt the message. (b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:9. Matrices can be used to send encrypted messages. Say you have a message matrix M and an
encryption matrix E. The encrypted message will be the product of those two matrices, i.e.
A = EM. In the matrix A, the numbers of M will be mangled with those of E. Unencrypting
the message requires performing the reverse operation to retrieve M from A.
You have been sent an encrypted message:
A =
m-20 a - 5e t-5v
-m+ 24 -a +6e -t+6v
and two possible encryption keys
=(-1)).
E₁ =
1
E₂ = -8
h-5a
-h+6a)
4 2
1 6
3-21
(a) Without performing any calculation, determine which of the encryption keys was used
to encrypt the message.
(b) Decrypt the message, i.e., find M from A using either E₁ or E2 in an appropriate way.
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