D. Micciancio, A Linear Space Algorithm for Computing the Hermite Normal Form, Proceedings ISSAC 2001, Lecture Notes in Computer Sci., 2146, Springer, New York, pp. 126-145, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....elements on the diagonal are strictly positive, and any other element b i;j satis es 0 b i;j b i;i . It is easy to see that every integer lattice L(B) has a unique basis in Hermite Normal Form, denoted HNF(B) Moreover, given any basis B for the lattice, HNF(B) can be eciently computed (see [23] for a recent algorithm and a survey of previous results) Notice that HNF(B) does not depend on the particular basis B with started from, and it is uniquely de ned by the lattice L(B) generated by B. For every basis B, the orthogonalized basis B = b 1 ; b n ] is de ned by ....

....of the major problems in GGH, requiring the application of LLL on a high dimensional matrix with very large entries. Here, key generation essentially consists of a Hermite Normal Form computation, a much simpler task than lattice reduction. Moreover, recent progress on the design of HNF algorithms [23] might lead to ecient key generation procedures. The most critical part of lattice based encryption schemes at this point is probably decryption. In this paper, and in our experiments we have used Babai s nearest plane algorithm [4] as we believe this is a quite natural choice. Although ....

D. Micciancio and B. Warinschi. A linear space algorithm for computing the Hermite Normal Form. In B. Mourrain, editor, International Symposium on Symbolic and Algebraic Computation. ACM, ACM, 2001. To Appear.

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D. Micciancio, A Linear Space Algorithm for Computing the Hermite Normal Form, Proceedings ISSAC 2001, Lecture Notes in Computer Sci., 2146, Springer, New York, pp. 126-145, 2001.

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