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LLL算法代码
以下为LLL算法的实现过程：（matlab代码）
本人在课程设计中完成以下工作
- LLL_exchange()函数
function [Y,square_length_Y_Y, Y_Y_coefficient] = LLL_exchange( k , Y , square_length_Y_Y , Y_Y_coefficient )
%UNTITLED2 此处显示有关此函数的摘要
% 此处显示详细说明disp('-----LLL_exchange---------start---------------------')kY% Y_Y_coefficient % square_length_Y_Yz = Y(k-1,:);Y(k-1,:) = Y(k,:);Y(k,:) = z;v = Y_Y_coefficient(k,k-1);siple = square_length_Y_Y(1,k) + v*v* square_length_Y_Y(1,k-1);Y_Y_coefficient(k,k-1) = v * square_length_Y_Y(1,k-1) / siple;square_length_Y_Y(1,k) = square_length_Y_Y(1,k) * square_length_Y_Y(1,k-1) / siple;square_length_Y_Y(1,k-1) = siple;%(4)for j=1:k-2t = Y_Y_coefficient(k-1,j);Y_Y_coefficient(k-1,j) = Y_Y_coefficient(k,j);Y_Y_coefficient(k,j) = t;end%(5)[n n] = size(square_length_Y_Y);for i= k+1:nE=Y_Y_coefficient(i,k) ;Y_Y_coefficient(i,k) = Y_Y_coefficient(i,k-1) - v * Y_Y_coefficient(i,k);Y_Y_coefficient(i,k-1) = Y_Y_coefficient(k,k-1) * Y_Y_coefficient(i,k) + E;enddisp('-----LLL_exchange---------end---------------------')end- LLL_reduced()函数
function [Y,Y_Y_coefficient] = LLL_reduced( k ,l ,Y , Y_Y_coefficient )
%UNTITLED3 此处显示有关此函数的摘要
% 此处显示详细说明disp('LLL_reduced--------start----------')klY% Y_Y_coefficient if abs( Y_Y_coefficient(k,l) ) > 0.5Y(k,:) = Y(k,:) - round( Y_Y_coefficient(k,l) ) * Y(l,:);for j=1:l-1Y_Y_coefficient(k,j) = Y_Y_coefficient(k,j) - round( Y_Y_coefficient(k,l) ) * Y_Y_coefficient(l,j) ;endY_Y_coefficient(k,l) = Y_Y_coefficient(k,l) - round( Y_Y_coefficient(k,l) );enddisp('LLL_reduced--------end----------')
end- LLL_main()函数
clc
clear
%Y=[-2 7 7 -5; 3 -2 6 -1;2 -8 -9 -7;8 -9 6 -4];
Y = [10305608 , -597165 , 45361210 , 39600006 , 12036060 -71672908 , 4156981 , -315467761, -275401230, -83709146-46304904 , 2685749 , -203811282, -177925680, -54081387-68449642 , 3969419 , -301282167, -263017213, -79944525-46169690 , 2677840 , -203215644, -177405867, -53923216 ]
%Y = [ 19, 2 , 32, 46, 3 , 33,
% 15, 42, 11, 0 , 3 , 24,% 43, 15, 0 , 24, 4 , 16,% 20, 44, 44, 0 , 18, 15,% 0 , 48, 35, 16, 31, 31,% 48, 33, 32, 9 , 1 , 29% ]
[n n] = size(Y) ;
Y_Y = zeros(n,n);
Y_Y_coefficient = zeros(n,n);
square_length_Y_Y = zeros(1,n);
format rat
for i=1:nY_Y(i,:) = Y (i,:);Y_Y_coefficient(i,i) = 1;for j=1:i-1Y_Y_coefficient(i,j) = dot( Y(i,:) , Y_Y(j,:) ) / square_length_Y_Y(1,j);Y_Y(i,:) = Y_Y(i,:) - Y_Y_coefficient(i,j) * Y_Y(j,:);endsquare_length_Y_Y(1,i) = dot( Y_Y(i,:) , Y_Y(i,:) );
end%---------------------Y_Y_coefficient
%---------------------square_length_Y_Y
disp('初次设置k=2----------------------------')
k=2while k<=n[Y,Y_Y_coefficient] = LLL_reduced(k,k-1,Y,Y_Y_coefficient);if square_length_Y_Y(1,k) >= (0.75 - Y_Y_coefficient(k,k-1) ^ 2 ) * square_length_Y_Y(1,k-1)for l=k-2:-1:1[Y, Y_Y_coefficient] = LLL_reduced(k,l,Y,Y_Y_coefficient);endk=k+1;else[Y,square_length_Y_Y, Y_Y_coefficient] = LLL_exchange( k , Y , square_length_Y_Y , Y_Y_coefficient );if k>2k=k-1 ;endend
Y
end
本文标签： LLL算法代码
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