| Latest revision |
Your text |
| Line 3: |
Line 3: |
| | |who=Joshua Brody | | |who=Joshua Brody |
| | }} | | }} |
| − | Cryptogenography, introduced by Brody et al. {{cite|BrodyJSW-14}}, is concerned with the following question: “How to share a secret without revealing the secret owner?”
| |
| − | In this problem, there are $k$ players and an eavesdropper. Input is a random bit $X \in \{0,1\}$, also called “the secret.” The secret owner $J$ is chosen uniformly at random from $[k]$. Players have private randomness and they can communicate publicly on a shared blackboard visible to everyone. Players are said to win if
| |
| − | * everyone learns the secret, and
| |
| − | * eavesdropper does not guess the secret owner correctly.
| |
| | | | |
| − | We are interested in maximizing the probability that players win (maximum success probability). For $k=2$, the following trivial protocol has success probability $0.25$. Just output $1$. It can be shown easily that maximum success probability is at most $0.5$. The bounds can be improved to $0.3384 \le $ maximum success probability $\le 0.361$. Here is a protocol that achieves success probability $1/3$.
| |
| | | | |
| − | ; <span>First round:</span>
| |
| − | : If Alice has the secret,
| |
| − | :* with probability $2/3$, she decides that Bob speaks in the second round
| |
| − | :* with probability $1/3$, she speaks in the second round.
| |
| − | :Else (if she does not have the secret)
| |
| − | :* with probability $1/3$, she decides that Bob speaks in the second round
| |
| − | :* with probability $2/3$, she speaks in the second round.
| |
| | | | |
| − | ; <span>Second round:</span>
| + | <references /> |
| − | : If the speaker has the secret, announce it. Otherwise, announce a random bit.
| |
| − | | |
| − | For large $k$, the following bounds can be shown: $0.5644 \le $ maximum success probability $\le 0.75$. Can we improve these bounds? For more information, including the state of the art bounds, see the papers of Jakobsen {{cite|Jakobsen-14}} and Doerr and Kunnemann {{cite|DoerrK-16}}.
| |
