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 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (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 -m+ 24 and two possible encryption keys E1 = t - 5v a - 5e a +6e -t+6v (18). 1 E₂ = -8 3 h-5a -h+6a) 4 21 16 -2 1 (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
Related questions
Question
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
-m+ 24
and two possible encryption keys
E1 =
t - 5v
a - 5e
a +6e -t+6v
(18).
1
E₂ = -8
3
h-5a
-h+6a)
4 21
16
-2 1
(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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 5 steps
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
for part b), how can you multiply the E1^-1 and A as they are not the same size matrix? is that possible?
Solution
by Bartleby ExpertFollow-up Question
for part (a) i don't understand how e2 can be used as the encryption key as the dimensions don't match either of the keys given as the message is a 2x4, while the keys are 2x2 and 3x3. they arent 2x4, so how could either of them be used?
Solution
by Bartleby ExpertRecommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
