In 1955, John Nash sent a remarkable letter to the National Security Agency, in which—seeking to build theoretical foundations for cryptography—he all but formulated what today we call the P=?NP problem, considered one of the great open problems of science. Here I survey the status of this problem in 2017, ... more >>>

We prove that \emph{at least} one of the following statements is true:

-- (Infinitely-often) Public-key encryption and key agreement can be based on injective one-way functions;
-- For every inverse polynomial $\epsilon$, the 4-round protocol from [Feige and Shamir, STOC 90] is distributional concurrent zero knowledge for any ... more >>>

We compare two methods for proving lower bounds on standard two-party model of communication complexity, the Rank method and Fooling set method. We present bounds on the number of functions $f(x,y)$, $x,y\in\{0,1\}^n$, with rank of size $k$ and fooling set of size at least k, $k\in [1,2^n]$. Using these bounds ... more >>>