Double Encryption Problem from Boneh/Shoup Textbook

coder

2/4/24, 7:32 PM

I am working on the following problem from the Boneh/Shoup textbook: 5.1 (Double encryption). Let E = (E,D) be a cipher. Consider the cipher E2 = (E2, D2), where E2(k,m) = E(k, E(k,m)). One would expect that if encrypting a message once with E is secure then encrypting it twice as in E2 should be no less secure. However, that is not always true.

(a) Show that there is a semantically secure cipher E such that E2 is not semantically secure.

(b) Prove that for every CPA secure ciphers E, the cipher E2 is also CPA secure. That is, show that for every CPA adversary A attacking E2 there is a CPA adversary B attacking E with about the same advantage and running time.

Picture attached:

0 + 1

multiple-encryption

Amit

2/4/24, 8:07 PM

(a) The one time pad. (b) .... :)

Elon Musk

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

EN: Double Encryption Problem from Boneh/Shoup Textbook

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.