帮我写一段用基础函数实现的可以成功运行的NTRU数字签名的MATLAB实验代码
时间: 2024-05-02 16:23:21 浏览: 22
好的,下面是一个基础函数实现的NTRU 数字签名的MATLAB 实验代码示例:
```
% 设置参数
N = 503; % 多项式系数数量
p = 3; % 模数
q = 64;
% 生成密钥对
[Kp, Ks] = ntru_gen_keypair(N, p, q);
% 现在我们可以进行签名和验证了
% 首先,我们需要一个消息
msg = 'Hello, world';
msg = uint8(msg); % 转换成数字类型
% 对消息进行签名
sig = ntru_sign(msg, Ks);
% 验证签名
v = ntru_verify(msg, sig, Kp);
% 输出结果
if v
disp('Signature is valid.');
else
disp('Signature is invalid.');
end
```
其中 `ntru_gen_keypair` 函数用于生成公钥和私钥,`ntru_sign` 函数用于对消息进行签名,`ntru_verify` 函数用于验证签名。
注意:代码中的 `N`、`p` 和 `q` 等参数需要根据具体情况做出相应的调整。
相关问题
帮我写一段用基础函数实现的NTRU数字签名功能的MATLAB代码
好的,我可以为您编写MATLAB代码来实现NTRU数字签名功能。以下是代码示例:
```matlab
% NTRU数字签名功能的MATLAB代码
function [ signature ] = ntru_signature( message, private_key )
% 定义NTRU参数
N = 503;
p = 3;
q = 64;
d = 45;
f = 3;
g = 3;
% 加载私钥
h = private_key.h;
f_inverse = private_key.f_inverse;
% 生成随机数P、R、E
P = randi([0,1],1,N);
R = randi([0,1],1,N);
E = randi([-1,0,1],1,N);
% 计算签名S
S = mod(p*f_inverse*(h.*R+mod(f.*P+g.*E,q)),q);
% 计算哈希值
hash = md5(message);
% 计算签名哈希
signature = mod(S+hash,q);
end
```
此代码实现了基础函数,使用NTRU参数和私钥对输入消息进行数字签名。注意:实际使用时,需要使用适当的参数和私钥生成函数来生成正确的参数和私钥。
帮我写一段用基础函数实现的NTRU数字签名的MATLAB代码
好的,以下是基础函数实现的NTRU数字签名的MATLAB代码。
```matlab
% Generate random keys for NTRU
N = 1024;
q = 2048;
d = 3;
N0 = ceil(log2(q));
N1 = N - N0 - 1;
N2 = N - N1 - 1;
f = 1 + x - x^3 - x^4 - x^6 + x^8;
g = 3 + x^2 - x^3 - x^5 + x^6 + x^8;
h = 1 - x;
% Choose a random message for signing
m = randi([0 1], 1, N1);
% Hash message
hash = mod(sum(m.*2.^(0:N1-1)), q);
% Generate random ephemeral key for signing
e = randi([-1 1], 1, N2);
% Calculate signature
f_inv = PolyInvMod(f, q, d);
a = PolyMulMod(f_inv, g, q, d);
b = PolyMulMod(a, e, q, d);
c = PolyMulMod(a, f_inv, q, d);
d = mod(q - hash - PolyEvalMod(b, h, q) + 2 * floor(q/2), q);
z = PolyAddMod(d * c, e, q);
% Verify signature
w = PolySubMod(PolyEvalMod(b, f, q), PolyEvalMod(z, h, q), q);
if w == hash
disp('VALID SIGNATURE');
else
disp('INVALID SIGNATURE');
end
% Polynomial multiplication modulo q with polynomial modulus f
function z = PolyMulMod(x, y, q, d)
z = mod(x * y, q);
for i = 1:d-1
z = PolyReduceMod(z, q);
end
end
% Polynomial addition modulo q
function z = PolyAddMod(x, y, q)
z = mod(x + y, q);
end
% Polynomial reduction modulo polynomial modulus f
function z = PolyReduceMod(x, q)
f = 1 + x - x^3 - x^4 - x^6 + x^8;
z = PolyMod(x, f, q);
end
% Polynomial division modulo q
function z = PolyDivMod(x, y, q)
[q1, r] = deconv(x, y);
z = mod(r, q);
end
% Polynomial modulo polynomial modulus f modulo q
function z = PolyMod(x, f, q)
while length(x) >= length(f)
if x(1) == 0
x = x(2:end);
continue;
end
shift = length(x) - length(f);
factor = x(1) * f;
factor = [zeros(1, shift), factor];
x = mod(PolySubMod(x, factor, q), q);
end
z = x;
end
% Polynomial subtraction modulo q
function z = PolySubMod(x, y, q)
z = mod(x - y, q);
end
% Inverse of polynomial x modulo q using Euclid's algorithm
function z = PolyInvMod(x, q, d)
[g, u, v] = ExtendedEuclid(x, q);
x_inv = mod(u * g^(d-1), q);
z = PolyMod(x_inv, x, q);
end
% Extended Euclid's algorithm
function [g, u, v] = ExtendedEuclid(a, b)
g0 = a; u0 = 1; v0 = 0;
g1 = b; u1 = 0; v1 = 1;
while g1 ~= 0
q = floor(g0 / g1);
temp = g0 - q * g1;
u2 = u0 - q * u1;
v2 = v0 - q * v1;
g0 = g1;
u0 = u1;
v0 = v1;
g1 = temp;
u1 = u2;
v1 = v2;
end
g = g0;
u = u0;
v = v0;
end
% Evaluate polynomial x modulo modulus m at point a using Horner's rule
function y = PolyEvalMod(x, a, m)
y = 0;
for i = length(x):-1:1
y = mod(x(i) + a * y, m);
end
end
```