Two researchers have improved a well-known technique for lattice basis reduction, opening up new avenues for practical experiments in cryptography and mathematics.
One important tool in this work is the LLL algorithm, named after the researchers who published it in 1982—Arjen Lenstra, Hendrik Lenstra Jr. and László Lovász. LLL, along with its many descendants, can break cryptographic schemes in some cases; studying how they behave helps researchers design systems that are less vulnerable to attack.
In a theoretical sense, the original LLL algorithm runs quickly: The time it takes to run doesn’t scale exponentially with the size of the input—that is, the dimension of the lattice and the size of the numbers in the basis vectors. But it does increase as a polynomial function, and “if you actually want to do it, polynomial time is not always so feasible,” said Léo Ducas, a cryptographer at the national research institute CWI in the Netherlands.
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