1 / 8

A More Efficient Algorithm for Lattice Basis Reduction

A More Efficient Algorithm for Lattice Basis Reduction. C.P.SCHNORR Journal of algorithm 9,47-62(1988) 報告者 張圻毓. Outline. LLL Algorithm Compare Time. LLL Algorithm. Input : Linearly independent column vector f 1 ……f n Z n Output :

fawn
Télécharger la présentation

A More Efficient Algorithm for Lattice Basis Reduction

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A More Efficient Algorithm for Lattice Basis Reduction C.P.SCHNORR Journal of algorithm 9,47-62(1988) 報告者 張圻毓

  2. Outline • LLL Algorithm • Compare • Time

  3. LLL Algorithm • Input : • Linearly independent column vector f1……fnZn • Output : • A reduced basis (b1……bn) of the lattice L=Σ1≦i ≦nZfiZn

  4. LLL Algorithm • 1. for i =1,…,n dobi fi • compute the GSO G*,M Qn*n , i  2 • 2.while i ≦n do • 3. for j= i-1,i-2,…,1 do • 4. bi  bi - 「μij」bj • update the GSO {replacement step}

  5. LLL Algorithm • 5. if i>1 and • then exchange bi-1 and bi and update • the GSO , i  i-1 • else i i+1 • 6. return b1,…,bn

  6. Compare • LLL algorithm • (i)滿足 ,1≦j＜i≦n • (ii)滿足 ，每一個基底元 • 素不會太小於前一個基底元素，一般δ為 • 3/4，則 所以會

  7. Compare • New basis reduction algorithm • (i)滿足 ,1≦j＜i≦n • (ii)滿足 ，則δ為 • 100/105大於原來數3/4， • (實際是1.538745)

  8. Time • LLL algorithm • arithmetic operation on • -bit • New algorithm • arithmetic operation on • -bit • (B bounds the euclidean length of the input vectors,ie )

More Related