A Note on Integer Factorization Using Lattices — mentioned by abetusk

Wed, 03 Mar 2021 22:30:03 GMT

OK, here is a brief overview for people: To factor a number N (assumed to essentially be the product of two very large primes), find a 'short' lattice vector [0] using LLL [1] (and BKZ reduction? [2]) that finds many relations of the form: (u_i) = p_i,0 * p_{i,1} * ... * p_{i,n-1} (u_i - v_i * N) = q_{i,0} * q_{i,1} * ... * q_{i,n-1} where p,q are small primes. Numbers that have all their factors less than some prime, B, are said to be "B-smooth". In the above, both (u_i) and (u_i - v_i * N) are p_{i,n-1}-smooth and q_{i,n-1}-smooth, respectively. Construct many u_i and (u_i - v_i * N), so…

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A Note on Integer Factorization Using Lattices — mentioned by abetusk