By Stephen J. Fink, Scott B. Baden (auth.), Yutaka Ishikawa, Rodney R. Oldehoeft, John V. W. Reynders, Marydell Tholburn (eds.)
This publication constitutes the refereed court cases of the 1st foreign convention on clinical Computing in Object-Oriented Parallel Environments, ISCOPE '97, held in Marina del Rey, California, in December 1997. the amount offers 36 revised papers conscientiously chosen for inclusion within the ebook. The papers handle run-time functionality optimization at numerous degrees, new language programming paradigms, functions of Java-based expertise, direct purposes in quite a few parts, object-oriented libraries, and new rules and techniques to parallel clinical computing. All in all, this can be an updated presentation of the state of the art within the software of object-oriented equipment in clinical and engineering applications.
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Extra info for Scientific Computing in Object-Oriented Parallel Environments: First International Conference, ISCOPE 97 Marina del Rey, California, USA December 8–11, 1997 Proceedings
Interestingly, even if the LLL “fudge factor” is 24 Glenn Durfee and Phong Q. Nguyen xy e3xy x2y x x2 x3y e3xyz y xy2 xy3 x2y3 x2y4 x3y4 x3y5 e3X2 e3x3y e3X3Y e3x3yz e3X3 – e2xyzf – e2x2yf – – – – – – exyzf2 – e2X2Y 2 e2X2Z – – – – – – – – – – – – – e2x2yzf e2X3Y 2 e2X3Z – – – – eX3Y 3 – – eX3Z2 e3y e3Y e3y2 e2yf y2 e3X2Y e3x2yz exyf2 x2y2 x2z x3y2 x3z x3y3 x3z2 e3X e3x2y e2xyf x3 e3XY e3Y 2 – e2y2f – – eyf2 – ey2f2 – yf3 – y2f3 – – – e2XY 2 – – – – – – – – – – – – – – – – – – – – – e2XY 3 – – – – – – – – – – eX2Y 3 – – – – eX2Y 4 – – – – – X3Y 4 – – – X3Y 5 Fig.
K. Lenstra, H. W. , and L. Lov´ asz. Factoring polynomials with rational coeﬃcients. , 261:513–534, 1982. 10. Waterloo Maple. The Maple computational algebra system for algebra, number theory and geometry. html. 11. W. Meier. Private communication. June, 2000. 12. P. Q. Nguyen and J. Stern. Lattice reduction in cryptology: An update. In Algorithmic Number Theory – Proc. of ANTS-IV, volume 1838 of LNCS. Springer-Verlag, 2000. 13. R. L. Rivest, A. Shamir, and L. M. Adleman. A method for obtaining digital signatures and public-key cryptosystems.
We have uq = ∆q1 ∆q2 mod p and therefore: qr uqr = ∆qr 1 ∆2 mod p, which can be rewritten as qr log(uqr ) = log(∆qr 1 ) + log(∆2 ) mod s, where the logarithms are with respect to ω qr . m1 We build a table T1 consisting of log(∆qr , and a table 1 ) for all ∆1 = 0, . . , 2 qr m2 T2 consisting of log(∆2 ) for all ∆2 = 0, . . , 2 . These tables are independent of ∆. The problem is now to express log(uqr ) as a modular sum t1 + t2 , where t1 ∈ T1 and t2 ∈ T2 . The number of targets t1 + t2 is 2m1 +m2 .
Scientific Computing in Object-Oriented Parallel Environments: First International Conference, ISCOPE 97 Marina del Rey, California, USA December 8–11, 1997 Proceedings by Stephen J. Fink, Scott B. Baden (auth.), Yutaka Ishikawa, Rodney R. Oldehoeft, John V. W. Reynders, Marydell Tholburn (eds.)