uestion 5
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
Question 5
![king the equalitr
Un
the pair (5, 16).
the integers V1 and V2:
Vi = 225 . 516 = 39· 40 = 12 (mod 43)
V2 = 313 = 12 (mod 43)
PROBLEMS 10.3
forwarded to a user with public key (47, 5, 10) and private key k = 19.
(a) If the random integer chosen for encryption is j = 13, determine the ciphero
(b) Indicate how the ciphertext can be decrypted using the recipient's private kev
2. Suppose that the following ciphertext is received by a person having ElGamal pubu
key (71, 7, 32) and private key k = 30:
%3D
%3D
(56, 45) (56, 38) (56, 29) (56, 03) (56, 67)
(56, 05) (56, 27) (56, 31) (56, 38) (56, 29)
Obtain the plaintext message.
The message NOT NOW (numerically 131419131422) is to be sent to a user of th
EIGamal system who has public key (37, 2, 18) and private key k = 17. If the intege=
j used to construct the ciphertext is changed over successive four-digit blocks from
j = 13 to j = 28 to j = 11, what is the encrypted message produced?
Assume that a person has ElGamal public key (2633, 3, 1138) and private key k = 965
If the person selects the random interger j = 583 to encrypt the message BEWARE OF
THEM, obtain the resulting ciphertext.
[Hint: 3583 = 1424 (mod 2633), 1138585 = 97 (mod 2633).]
5. (a) Aperson with public key (31, 2, 22) and private key k = 17 wishes to sign a message
whose first plaintext block is B = 14. If 13 is the integer chosen to construct uie
signature, obtain the signature produced by the ElGamal algorithm.
(b) Confirm the validity of this signature.
3.
%D
%3D
ewollol l](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2F378d5c6a-790e-46a5-98ad-fa97b1e1b53a%2Fuxb8yjo.jpeg&w=3840&q=75)
Transcribed Image Text:king the equalitr
Un
the pair (5, 16).
the integers V1 and V2:
Vi = 225 . 516 = 39· 40 = 12 (mod 43)
V2 = 313 = 12 (mod 43)
PROBLEMS 10.3
forwarded to a user with public key (47, 5, 10) and private key k = 19.
(a) If the random integer chosen for encryption is j = 13, determine the ciphero
(b) Indicate how the ciphertext can be decrypted using the recipient's private kev
2. Suppose that the following ciphertext is received by a person having ElGamal pubu
key (71, 7, 32) and private key k = 30:
%3D
%3D
(56, 45) (56, 38) (56, 29) (56, 03) (56, 67)
(56, 05) (56, 27) (56, 31) (56, 38) (56, 29)
Obtain the plaintext message.
The message NOT NOW (numerically 131419131422) is to be sent to a user of th
EIGamal system who has public key (37, 2, 18) and private key k = 17. If the intege=
j used to construct the ciphertext is changed over successive four-digit blocks from
j = 13 to j = 28 to j = 11, what is the encrypted message produced?
Assume that a person has ElGamal public key (2633, 3, 1138) and private key k = 965
If the person selects the random interger j = 583 to encrypt the message BEWARE OF
THEM, obtain the resulting ciphertext.
[Hint: 3583 = 1424 (mod 2633), 1138585 = 97 (mod 2633).]
5. (a) Aperson with public key (31, 2, 22) and private key k = 17 wishes to sign a message
whose first plaintext block is B = 14. If 13 is the integer chosen to construct uie
signature, obtain the signature produced by the ElGamal algorithm.
(b) Confirm the validity of this signature.
3.
%D
%3D
ewollol l
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