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。

% 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