Blomer and Naewe[BN09] modified the randomized sieving algorithm of Ajtai, Kumar and Sivakumar[AKS01] to solve the shortest vector problem (SVP). The algorithm starts with $N = 2^{O(n)}$ randomly chosen vectors in the lattice and employs a sieving procedure to iteratively obtain shorter vectors in the lattice. The running time of the sieving procedure is quadratic in $N$. We study this problem ...

The security of the RSA cryptosystem depends on the difficulty of factoring large integers. The best current factoring algorithm is the Number Field Sieve (NFS), and its most difficult part is the sieving step. In 1999 a large distributed computation involving hundreds of workstations working for many months managed to factor a 512-bit RSA key, but 1024-bit keys were believed to be safe for the...

These are notes on a preliminary follow-up to a question of Jim Propp, about cyclic sieving of cyclic codes. We show that two of the Mahonian polynomials are cyclic sieving polynomials for certain Dual Hamming Codes: X and X inv for q = 2, 3 and q = 2, respectively.

The case of a patient with an air gun pellet injury to the right colon is reported. This was treated conservatively, and the pellet was passed per rectum 12 hours after the injury. Gunshot wounds to the abdomen do not necessarily warrant immediate laparotomy. Sieving of bowel motions may identify if the foreign body has been passed.

The purpose of this study was to evaluate the influence of variables in a flotation technique for the recovery of Toxocara canis eggs from soil. The trials were done under standardized conditions on one gram of previously sterilized soil samples contaminated with 200 eggs of T. canis. The following variables were evaluated in serial steps: sieving; type of wash; time of stirring; resuspension o...

The cyclic sieving phenomenon of Reiner, Stanton, and White characterizes the stabilizers group actions on finite sets using q-analogue polynomials. Eu Fu demonstrated a generalized cluster complexes every type q-Catalan numbers. In this paper, we exhibit dihedral phenomenon, introduced for odd n by Rao Suk, clusters type. A case, show that Raney numbers count both reflection-symmetric k-angula...