the equality of the pair (5, 16). On its arrıval, the integers V1 and V2: V = 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...

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Extracted text: the equality of the pair (5, 16). On its arrıval, the integers V1 and V2: V = 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 (a) If the random integer chosen for encryption is j = 13, determine the cipher (b) Indicate how the ciphertext can be decrypted using the recipient's private ko 2. Suppose that the following ciphertext is received by a person having ElGamal puki key (71, 7, 32) and private key k = 30: 19. %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. 3. The message NOT NOW (numerically 131419131422) is to be sent to a user of the ElGamal 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 EIGamal 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), 1138583 = 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 %3D oliol