Alice and Bob are using Elgamal to communicate with prime p = 48112959837082048697 and B = 30980566787060881636. Here’s a transcript of a recent communication. Bob: Alice, you know how much I care about you. You know I can be trusted. Won’t you tell me your phone number? Alice: I don’t want everyone at work to know. Let me encrypt it. Here you go: (17338469904166832757, 8068454082369421991). Bob: Wow, that was fast! You’re so good at encryption protocols. . . . During the interlude while Bob decrypts, Alice sends text messages to her mom with pictures of her new puppy, Woof . . . Bob: Wait, that’s your work number, 1-315-312-6586. Alice: Oh, sorry. Here’s my cell number: (41718705614960107467, 21459087071846659484). Bob: You are so quick with the encryption! How do you do that? Alice: Oh, I set the encryption program to get a new ephemeral key just by doubling the last one. It really speeds things up compared to the default method. Edgar was listening in the whole time. Show how Edgar is able to figure out the plaintext of the second message, without figuring out b or solving any discrete log problem at all. The plaintext is not the complete answer.
Alice and Bob are using Elgamal to communicate with prime p = 48112959837082048697 and
B = 30980566787060881636. Here’s a transcript of a recent communication.
Bob: Alice, you know how much I care about you. You know I can be trusted.
Won’t you tell me your phone number?
Alice: I don’t want everyone at work to know. Let me encrypt it. Here you go:
(17338469904166832757, 8068454082369421991).
Bob: Wow, that was fast! You’re so good at encryption protocols.
. . . During the interlude while Bob decrypts, Alice sends text messages to her mom
with pictures of her new puppy, Woof . . .
Bob: Wait, that’s your work number, 1-315-312-6586.
Alice: Oh, sorry. Here’s my cell number: (41718705614960107467, 21459087071846659484).
Bob: You are so quick with the encryption! How do you do that?
Alice: Oh, I set the encryption program to get a new ephemeral key just by doubling
the last one. It really speeds things up compared to the default method.
Edgar was listening in the whole time. Show how Edgar is able to figure out the plaintext of
the second message, without figuring out b or solving any discrete log problem at all.
The plaintext is not the complete answer.
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