Cryptographic Protocols Notes for Lecture 2 Scribe :

Algorithms are commonly formalized as Turing machines, which are the basis for defining notions such as running time and space complexity; the exact formalism, however, is of no concern in this lecture. For our purposes, an algorithm A takes some input x ∈ {0, 1}∗, performs some computation, and outputs a value A(x). Running time and space complexity of an algorithm are measured as a function of the length |x| of its input x. An algorithm is called efficient if its running time is bounded by a polynomial (and thus also its space complexity); an algorithm with an arbitrary running time is called unbounded. An algorithm with access to uniform random bits during its computation is called probabilistic or randomized and deterministic otherwise.