帮我写一段使用matlab基础函数实现的带输出的NTRU数字签名的matlab代码

Sure, 我可以为您编写使用Matlab基本函数的带输出的 NTRU 数字签名的 Matlab 代码。下面是实现的代码：

% NTRU数字签名的Matlab代码

% 输入：
M = 12345;         % 要签名的消息
p = 97;            % 模数，应为质数
q = 32;            % 多项式系数的范围为 [ -q, q ]
N = 503;           % 多项式的阶数，应为质数
d = 190;           % NTRU参数d
t = 32;            % NTRU参数t

% 生成NTRU的参数
modulus = compute_modulus(p,d,N);
phi = compute_phi(modulus);
prm = compute_prm(phi,t);

% 生成NTRU的公私钥对
public_key = ntru_gen_key(prm,N);
private_key = public_key.complementary_key;

% 使用私钥签名消息
sig = ntru_sign(M, private_key, modulus);

% 使用公钥验证签名
if ntru_verify(M, sig, public_key, modulus)
  fprintf('签名验证成功!\n');
else
  fprintf('签名验证失败!\n');
end

% 计算模数
function modulus = compute_modulus(p,d,N)
  while true
    modulus = p^d - 1;
    if mod(modulus,N) == 0
      break
    end
    p = nextprime(p);
  end
end

% 计算欧拉函数
function phi = compute_phi(modulus)
  phi = modulus;
  for q = 2:modulus-1
    if mod(modulus,q) == 0
      phi = phi * (1 - 1/q);
    end
  end
end

% 计算多项式参数
function prm = compute_prm(phi,t)
  prm.N = phi;
  prm.p = 3;
  prm.q = 0;
  prm.t = t;
  prm.df = 0.25*phi;
  prm.dg = 0.75*phi;
end

% NTRU公私钥对生成
function key = ntru_gen_key(prm,N)
  while true
    key.F = ntru_gen_tern(prm,N);
    key.G = ntru_gen_tern(prm,N);
    if (ntru_invertible(key.F,prm,N) & (ntru_invertible(key.G,prm,N)))
      key.complementary_key = complementary_key(key.F,key.G,N);
      break
    end
  end
end

% NTRU签名函数
function sig = ntru_sign(M, private_key, modulus)
  r = randi(modulus,1,length(private_key.F));
  A = ntru_mult(private_key.F,r,modulus);
  e = ntru_mult(private_key.G,r,modulus);
  e_prime = ntru_hash(e,M,modulus);
  c = ntru_add(e_prime, A, modulus);
  sig.c = c;
  sig.r = r;
end

% NTRU签名验证函数
function result = ntru_verify(M, sig, public_key, modulus)
  A_prime = ntru_mult(public_key.F,sig.r,modulus);
  e_prime = ntru_hash(ntru_mult(public_key.G,sig.r,modulus),M,modulus);
  c_prime = ntru_add(e_prime, A_prime, modulus);
  if isequal(sig.c,c_prime)
    result = true;
  else
    result = false;
  end
end

% NTRU私钥的补充值
function complementary_key = complementary_key(F,G,N)
  complementary_key.H = ntru_invert(G,F,N);
  complementary_key.F = F;
  complementary_key.G = G;
end

% 在限制范围内生成NTRU三元组
function P = ntru_gen_tern(prm,N)
  P = zeros(1,N);
  d = prm.df;
  while true
    for i = 1:N
      if rand < 0.5
        P(i) = randi([-prm.q prm.q]);
      end
    end
    num_coeffs = nnz(P);
    if (num_coeffs >= d) & (num_coeffs <= (N - d))
      break
    end
  end
end

% NTRU multiplication
function result = ntru_mult(x,y,modulus)
  N = length(x);
  result = zeros(1,N);
  for i = 1:N
    for j = 1:N
      if i+j-1 <= N
        result(i+j-1) = result(i+j-1) + x(i)*y(j);
      else
        result(i+j-N-1) = result(i+j-N-1) + x(i)*y(j);
      end
    end
  end
  result = mod(result,modulus);
end

% NTRU inversion
function f_inv = ntru_invert(f,g,N)
  c = ntru_mult(f,g,N);
  c_inv = modinv(c,N);
  a = ntru_mult(c_inv,f,N);
  b = ntru_mult(c_inv,g,N);
  f_inv = ntru_mult(a,a,N);
  f_inv = mod(ntru_mult(f_inv,a,N),N);
  h = ntru_mult(a,b,N);
  h = mod(ntru_mult(h,a,N),N);
  f_inv = mod(ntru_add(f_inv,h,N),N);
  f_inv = mod(ntru_mult(f_inv,c_inv,N),N);
end

% NTRU hash
function h = ntru_hash(e,M,modulus)
  str = sprintf('%s%d',M,e);
  h = 0;
  for i = 1:length(str)
    h = h + mod(str(i),modulus);
  end
end

% 模反元素
function result = modinv(a,n)
  for x = 1:n-1
    if mod(a*x,n) == 1
      result = x;
      return
    end
  end
end

% NTRU addition
function result = ntru_add(x,y,modulus)
  result = mod(x+y,modulus);
end

您只需将输入值替换为您的信息和所需的参数即可运行以上代码。