npojd 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), 1138ɔ83 = 97 (mod 2633).] %3D %3D to (a) A nerson with nublio 1
npojd 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), 1138ɔ83 = 97 (mod 2633).] %3D %3D to (a) A nerson with nublio 1
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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![and thereafter solves the congruence
25d = 13 – 5 · 15 (mod 42)
the integers V1 and V2:
VI = 225. 516 = 39 · 40 = 12 (mod 43)
V2 = 313 = 12 (mod 43)
PROBLEMS 10.3
1.
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 ciphertext
(b) Indicate how the ciphertext can be decrypted using the recipient's private key.
2. Suppose that the following ciphertext is received by a person having ElGamal public
key (71, 7, 32) and private key k = 30:
%3D
(56, 45) (56, 38) (56, 29) (56, 03)
(56, 67)
5. 67)
(56, 05) (56, 27) (56, 31) (56, 38) (56, 29) n
Obtain the plaintext message.
3. The message NOT NOW (numerically 131419131422) is to be sent to a user of the
EIGamal system who has public key (37, 2, 18) and private key k = 17. If the integer
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?
4. Assume that a person has ElGamal public key (2633, 3, 1138) and private key k = 965.
person selects the random interger j = 583 to encrypt the message BEWARE OF
THEM, obtain the resulting ciphertext.
[Hint: 3583 = 1424 (mod 2633), 1138083 = 97 (mod 2633).]
5. (a) A person 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 the
signature, obtain the signature produced by the ElGamal algorithm.
(b) Confirm the validity of this signature.
%3D
%3D
%3|
If the
to
%3D
ewoliol s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c7b497-dac7-4855-b923-2e60bbc73063%2F829dcd57-4099-49bf-809e-a8b992cfcc62%2F62u6m78.jpeg&w=3840&q=75)
Transcribed Image Text:and thereafter solves the congruence
25d = 13 – 5 · 15 (mod 42)
the integers V1 and V2:
VI = 225. 516 = 39 · 40 = 12 (mod 43)
V2 = 313 = 12 (mod 43)
PROBLEMS 10.3
1.
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 ciphertext
(b) Indicate how the ciphertext can be decrypted using the recipient's private key.
2. Suppose that the following ciphertext is received by a person having ElGamal public
key (71, 7, 32) and private key k = 30:
%3D
(56, 45) (56, 38) (56, 29) (56, 03)
(56, 67)
5. 67)
(56, 05) (56, 27) (56, 31) (56, 38) (56, 29) n
Obtain the plaintext message.
3. The message NOT NOW (numerically 131419131422) is to be sent to a user of the
EIGamal system who has public key (37, 2, 18) and private key k = 17. If the integer
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?
4. Assume that a person has ElGamal public key (2633, 3, 1138) and private key k = 965.
person selects the random interger j = 583 to encrypt the message BEWARE OF
THEM, obtain the resulting ciphertext.
[Hint: 3583 = 1424 (mod 2633), 1138083 = 97 (mod 2633).]
5. (a) A person 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 the
signature, obtain the signature produced by the ElGamal algorithm.
(b) Confirm the validity of this signature.
%3D
%3D
%3|
If the
to
%3D
ewoliol s
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