Rigorous Running Time
The Schnorr-Seysen-Lenstra probabilistic algorithm has been rigorously proven by Lenstra and Pomerance to have expected running time by replacing the GRH assumption with the use of multipliers. The algorithm uses the class group of positive binary quadratic forms of discriminant Δ denoted by GΔ. GΔ is the set of triples of integers (a, b, c) in which those integers are relative prime.
Read more about this topic: Integer Factorization Algorithms
Famous quotes containing the words rigorous, running and/or time:
“What is the most rigorous law of our being? Growth. No smallest atom of our moral, mental, or physical structure can stand still a year. It grows—it must grow; nothing can prevent it.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Kicking the heart
with pain’s big boots running up and down
the intestines like a motorcycle racer.”
—Anne Sexton (1928–1974)
“When I go into a museum and see the mummies wrapped in their linen bandages, I see that the lives of men began to need reform as long ago as when they walked the earth. I come out into the streets, and meet men who declare that the time is near at hand for the redemption of the race. But as men lived in Thebes, so do they live in Dunstable today.”
—Henry David Thoreau (1817–1862)