2.8. Alice and Bob agree to use the prime p = 1373 and the base g = 2 for communications using the ElGamal public key cryptosystem. (a) Alice chooses a = 947 as her private key. What is the value of her public key A? (b) Bob chooses b = 716 as his private key, so his public key is B = 27¹6 = 469 (mod 1373). Alice encrypts the message m = 583 using the ephemeral key k = 877. What is the ciphertext (C₁, C2) that Alice sends to Bob? (c) Alice decides to choose a new private key a = 299 with associated public key A = 22⁹9⁹ = 34 (mod 1373). Bob encrypts a message using Alice's public key and sends her the ciphertext (c₁, c2) = (661, 1325). Decrypt the message.
2.8. Alice and Bob agree to use the prime p = 1373 and the base g = 2 for communications using the ElGamal public key cryptosystem. (a) Alice chooses a = 947 as her private key. What is the value of her public key A? (b) Bob chooses b = 716 as his private key, so his public key is B = 27¹6 = 469 (mod 1373). Alice encrypts the message m = 583 using the ephemeral key k = 877. What is the ciphertext (C₁, C2) that Alice sends to Bob? (c) Alice decides to choose a new private key a = 299 with associated public key A = 22⁹9⁹ = 34 (mod 1373). Bob encrypts a message using Alice's public key and sends her the ciphertext (c₁, c2) = (661, 1325). Decrypt the message.
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a,b,c,d if possible
Transcribed Image Text:2.8. Alice and Bob agree to use the prime p = 1373 and the base g
communications using the ElGamal public key cryptosystem.
(a) Alice chooses a = 947 as her private key. What is the value of her public key A?
(b) Bob chooses b = 716 as his private key, so his public key is
B = 27¹6 = 469 (mod 1373).
= 2 for
Alice encrypts the message m = 583 using the ephemeral key k = 877. What
is the ciphertext (C₁, C₂) that Alice sends to Bob?
(c) Alice decides to choose a new private key a = 299 with associated public key
A = 22⁹⁹ = 34 (mod 1373). Bob encrypts a message using Alice's public key
and sends her the ciphertext (C₁, C2) = (661, 1325). Decrypt the message.
(d) Now Bob chooses a new private key and publishes the associated public key B =
893. Alice encrypts a message using this public key and sends the ciphertext
(C1, C₂) (693, 793) to Bob. Eve intercepts the transmission. Help Eve by
solving the discrete logarithm problem 26 = 893 (mod 1373) and using the value
of b to decrypt the message.
=
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