There is a probabilistic

polynomial-time algorithm TrapGen(q,n) that outputs a pair ([mathematical expression not reproducible]) such that A is statistically close to a uniform matrix in [mathematical expression not reproducible] and S is a basis for [mathematical expression not reproducible] satisfying

XP: For every fixed value of the parameter k, there exists a

polynomial-time algorithm solving the problem on inputs of size n, but the exponent of the running time grows with k, i.

m])n , any probabilistic

polynomial-time algorithm B, and any sufficiently large k,

ver], [epsilon]')-secure against adaptive chosen ciphertext attacks in the random oracle model if there exists no probabilistic

polynomial-time algorithm B that can (t, [epsilon])-break the RSA problem, where

Then the Quadratic Residue Assumption [3] states that there is no probabilistic

polynomial-time algorithm for computing square roots with respect to modulus N.

There is a new appendix on the recently discovered unconditional deterministic

polynomial-time algorithm for primality testing.

There exists a

polynomial-time algorithm for the prefetch/caching problem on D parallel disks, that produces a solution with at most D times the optimum stall time using at most D - 1 extra memory locations.

Hochbaum and Maass [1985] gave a

polynomial-time algorithm to compute a cover of size (1 + [Epsilon])k*, for any [Epsilon] [is greater than] 0 [1985]; see also Bronnimann and Goodrich [1995], Feder and Greene [1988], and Gonzalez [1991].

The long standing open question, "whether there can be any

polynomial-time algorithm for LP" was resolved when Khachian developed the ellipsoid algorithm.

The CLS scheme is proven existentially unforgeable against strong adversaries in random oracle model, under the assumption the [gamma]-Ideal-SVP against

polynomial-time algorithm is hard.

Sundararaghavan and Ahmed [7] developed a

polynomial-time algorithm to determine the optimal job-machine assignment for identical parallel machines.

A problem may remain NP-hard even if restricted to instances with a particular value of the parameter, or there may be a

polynomial-time algorithm for each such value.