Score:1

Elliptic curve ElGamal cryptosystems

sm flag

I have been working through a book on cryptography and have recently come across elliptic curves. This particular question has me stumped and the book isn't much help, unfortunately. I was wondering if someone was able to talk me through the process a little better. The question is:

Alice and bob use

  • the prime p=83,
  • an elliptic curve E: y^2 = x^3 + 5x + c (mod 83),
  • and point P=(3,11) on E.

Alice chose k=2 but she needs help choosing her public key (p,P,Q,E) where Q = kP (mod p). Find c so that the point P is on E, and find the point Q and the curve E. Also bob sends Alice the pair ((5, 48), (13, 10)). What is the message?

If there is a good resource for learning this style of the question then any suggestion is greatly appreciated! Thanks!

I sit in a Tesla and translated this thread with Ai:

mangohost

Post an answer

Most people don’t grasp that asking a lot of questions unlocks learning and improves interpersonal bonding. In Alison’s studies, for example, though people could accurately recall how many questions had been asked in their conversations, they didn’t intuit the link between questions and liking. Across four studies, in which participants were engaged in conversations themselves or read transcripts of others’ conversations, people tended not to realize that question asking would influence—or had influenced—the level of amity between the conversationalists.