probabilistic polynomial 
A probabilistic polynomialtime prover with the appropriate trapdoor knowledge is sufficient.


This treatment is appropriate for cryptographic settings modeled by probabilistic polynomialtime machines.


[ACGS] that the following problems are equivalent by probabilistic polynomial time reductions: (1) given EN(x) find x; (2) given EN(x) predict the leastsignificant bit of x with success probability 1/2 + 1/poly(n) , where N has n bits.


The security guarantee holds with respect to probabilistic polynomialtime adversaries that control the communication channel (between the parties), and may omit, insert, and modify messages at their choice.


We introduce generalized notions of low and high complexity classes and study their relation to structural questions concerning bounded probabilistic polynomialtime complexity classes.


We show, for example, that for a bounded probabilistic polynomialtime complexity class


We construct a probabilistic polynomial time algorithm that computes the mixed discriminant of given n positive definite matrices within a 2O(n) factor.


As a corollary, we show that the permanent of an nonnegative matrix and the mixed volume of n ellipsoids in Rn can be computed within a 2O(n) factor by probabilistic polynomial time algorithms.


Because we deal with probabilistic polynomial time adversaries, we can assume that the bit errors follow a computationally bounded distribution.


Clearly, B runs in probabilistic polynomial time as so does A.


Clearly, B runs in probabilistic polynomial time as does A.


Formally, a certisignature scheme consists of 6 probabilistic polynomial time algorithms.


Here the attacker is assumed to run in probabilistic polynomial time and the success of a forgery to have a nonnegligible probability.


Perhaps we should now equate the efficiently computable problems with the class of problems solve in probabilistic polynomial time.


The computational power of the adversary is modeled by a probabilistic polynomial time Turing machine.


We denote the probabilistic polynomialtime as ppt and we call the algorithm efficient if its running time is polynomial.

