For real numbers C, T 1 , T 2 , ... we find all solutions µ to the stochastic fixed point equation W j≥1 T j W j + C, where W, W 1 , W 2 , ... are independent real-valued random variables with distribution µ and means equality in distribution. All solutions are infinitely divisible. The set of solutions depends on the closed multiplicative subgroup of R * = R\{0} generated by the T j. If this g...

We show that $T \bar T, J T$ and $J T_a$ - deformed classical CFTs possess an infinite set of symmetries take the form a field-dependent generalization two-dimensional conformal transformations. If, in addition, seed affine $U(1)$ symmetry, we it also survives theories, again form. These can be understood as infinitely-extended underlying CFT, seen through prism "dynamical coordinates" characte...

Scheme. Gentry starts with a definition of an abstract scheme using rings and ideals, omitting instantiation details at first. His scheme is as follows (additional remarks appear after the description): KeyGen(R,BI). On input a ring R and the basis BI of an ideal I, this randomised algorithm generates via (Bsk J , B pk J ) ←R IdealGen(R,BI) two bases for an ideal J and outputs the public key pk...

Password Authenticated Key Exchange (PAKE) is one of the important topics in cryptography. It aims to address a practical security problem: how to establish secure communication between two parties solely based on a shared password without requiring a Public Key Infrastructure (PKI). After more than a decade of extensive research in this field, there have been several PAKE protocols available. ...