34 problems

Generalized capacity comparison conjecture. For every joint distribution $P_{X,Y,Z,X',Y',Z'}$,

Tyagi's public-communication conjecture. Any such protocol must reveal publicly at least

Maurer–Wolf conjecture. The secret-key capacity vanishes if and only if the intrinsic information vanishes:

XOR non-achievability conjecture. For some, or equivalently in the paper's general formulation for a general distribution $P_{X,Y}$, the rate $I(X;Y)$ is not achievable:

Let $\upsilon,\upsilon_2,\upsilon_3,\ldots$ be the weighted-average ITV family defined in the source, and let the row-column-type transformations be the transformations on the tran…

Let $XYZ$ be the candidate distribution described immediately before the claim, and let $P_{\overline{X}|X}$ and $P_{\overline{Y}|Y}$ range over binarization channels. The Z-shaped…

Let $XYZ$ be the distribution displayed in the source, depending on a parameter $a$. The candidate-distribution binarization conjecture. There exists a value $a$ such that, for eve…

Let $a_{ij}:=P_{\overline{Y^2}|Y^2}(0,rs)$ for $r,s\in\{1,2,3\}$, and define $\tau_2$ on the indicated set by … where $j=\left\lceil i/2\right\rceil$ for $1\leq i\leq6$, and … The…

Let $X,Y,Z$ have the distribution specified in the source, with $Z$ determined by $X$ and $Y$ according to the displayed table. For $N\geq1$, let $\overline{Y^N}$ be any binary out…

Let $X,Y,Z$ be jointly distributed, and let $\overline{X}$ and $\overline{Y}$ be binary outputs of arbitrary binary output channels applied to $X$ and $Y$. For $N\geq 1$, let…

Let $X,Y,Z$ be jointly distributed random variables, and let $S(X:Y||Z)$ denote the secret-key rate and $I(X:Y \downarrow Z)$ the intrinsic information. The bound-secrecy conjectur…

Let $P_{XYZ}$ be a probability distribution. The Renner–Wolf conjecture. … The reduced intrinsic information is a known upper bound on the secret-key rate and can be strictly small…

The paper studies three-party secret key agreement with simultaneous messages, where the parties' inputs have specified information-complexity profiles. Adaptation conjecture. The…

Let $(\mathord{Z}_V,\mathord{Z}_{\mathrm{w}})$ be a multiterminal source with wiretapper side information. Write $R_{\mathrm{L}}$ for the minimum leakage rate for secure omniscienc…

Consider the DSBE source described in the preceding lemma, with $C_{\mathrm{W}}^{(r)}$ the wiretap secret key capacity and $R_{\mathrm{L}}^{(r)}$ the minimum leakage rate when at m…

Let $(\mathord{Z}_V,\mathord{Z}_{\mathrm{w}})$ be a finite linear source, and let $R_{\mathrm{L}}$ denote its minimum leakage rate for secure omniscience and $C_{\mathrm{W}}$ its w…

Linear-decay conjecture. The unquantized secret-key capacity decreases at most linearly in the channel quality ratio, unlike the quantized secret-key capacity, which decreases at l…

For a finite linear source, let $C_{\operatorname{W}}$ denote its wiretap secret key capacity. Secure omniscience is a communication protocol in which the users enable all terminal…

Consider a multiterminal secret key agreement problem with several active users, no helpers, no silent users, and no wiretapper's side information. Let the users observe their resp…

Unique information lower-bound conjecture. The unique information lower bounds the two-way secret key rate:

Let $C_{\operatorname{S}}(0)$ denote the secrecy capacity when the total public discussion rate is asymptotically zero, and let $J_{\operatorname{GK}}(\mathbf{Z}_V)$ denote the mul…

Let $R_{\op{S}}$ be the minimum communication rate required to achieve the secrecy capacity in the secret-key agreement model. A trusted helper is a user whose source is trusted an…

Let $R_{\op{S}}$ denote the minimum communication rate needed to achieve the secrecy capacity in the multiterminal secret-key agreement model. Users are vocal when they communicate…

Let $V=[6]$ and let $r_{\operatorname{K}}$ and $r_V=(r_i:i\in V)$ denote the secret-key rate and discussion-rate vector, respectively. Write … Let $\mathcal R$ denote the achievabl…

Let $V=[6]$, and let the terminal observations be … Here $r_{\operatorname{K}}$ is the secret-key rate, $r_V$ is the vector of discussion rates, and $r(V)=\sum_{i\in V}r_i$ is the…