Reference no: EM132278149

Hiding vs. binding commitments: Bob is launching a new secure messaging app, BobCrypt. When Alice installs the app, it creates an account for her on the BobCrypt server using a hash of her phone number. The app then queries the server by sending the hash of each phone number in Alice's address book to learn which of Alice's friends already have BobCrypt accounts. The goal is that users can discover their friends' accounts without the server learning the contents of every user's address books.

a. Explain why this scheme does not achieve the intended security goal. How can Bob act maliciously to determine the phone numbers and contacts of all BobCrypt users?

b. After you tell Bob that a simple hash is a binding commitment, but does not hide the committed value, he decides to use a common construction for hiding commitments in Bob Crypt 2.0 . The app now uploads H(phone number, r) where r is a random 128-bit nonce chosen by the app. Explain to Bob why it is not possible to provide the intended functionality using this approach.