帮我写一段用基础函数实现的比较低阶的NTRU数字签名的MATLAB代码
时间: 2024-05-23 10:09:47 浏览: 15
好的,以下是用基础函数实现的比较低阶的NTRU数字签名的MATLAB代码:
% Step 1: Generate public and private keys
N = 31; % Length of the polynomial
p = 3; % Modulus
q = 16; % Rescaling factor
f = genf(N,p,q); % Generate f
g = BinaryToString(fqm(f,q,N),p); % Compute g
F = fqm(f,p,N); % Generate F
h = genh(F,g,N); % Compute h
sk = ModReduce(randn(1,N),p); % Generate secret key
pk = [h,ModReduce(sk*g, p)]; % Generate public key
% Step 2: Sign a message
msg = 'Hello, world!'; % The message to be signed
K = BinaryToString(fqm(genf(N,2,1),2,N)); % Generate K, the random seed
r = ModReduce(fqm(GenRandomTernary(N),2,N),p); % Generate r
e = ModReduce(fqm(GenRandomTernary(N),2,N),p); % Generate e
A = ModReduce(fqm(qr(0,N-1),2,N),p); % Set A to the zero polynomial
B = ModReduce(sk*r + e + fqm(StringToBinary(msg),p,N)*A, p); % Compute B
InvF = ModInverse(F, p); % Compute the inverse of F modulo p
S = ModReduce(r + F*ModReduce(InvF*B - sk*e, p), p); % Compute the signature
% Step 3: Verify the signature
if (VerifySignature(S, StringToBinary(msg), pk, q, p, N) == 1)
disp('Signature verified successfully!')
else
disp('Signature verification failed!')
end
% ------------------ Helper functions ------------------
function f = genf(N, p, q)
f = zeros(1,N);
f(1) = 1;
f(N/2 + 1) = -1;
while true
f(2:N/2) = GenRandomTernary(N/2);
if (ModReduce(fqm(f,p,N),q,N) ~= 0)
break
end
end
end
function h = genh(F, g, N)
InvF = ModInverse(F, 3);
h = ModReduce(fqm(InvF*g,3,N),2,N);
end
function t = GenRandomTernary(N)
t = zeros(1,N);
nonzero_indices = randperm(N, ceil(N/3));
t(nonzero_indices) = randsample([-1 1], ceil(N/3), true);
end
function y = fqm(x, q, N)
y = ModReduce(q*ModReduce(x,2,N) - ModReduce(q-1,2,N),q,N);
end
function y = ModReduce(x, p)
y = mod(x,p);
y(y>p/2) = y(y>p/2) - p;
end
function y = ModInverse(x, p)
[gcd,inv1,inv2] = gcdex(x,p);
y = mod(inv1, p);
end
function y = BinaryToString(x, p)
y = char(mod(x,p) + 65);
end
function y = StringToBinary(x)
y = zeros(1,length(x));
for i = 1:length(x)
y(i) = x(i) - 65;
end
end
function y = VerifySignature(S, msg, pk, q, p, N)
InvF = ModInverse(fqm(pk(1:N),p,N),p);
inv_h_sk = ModReduce(fqm([pk(N+1:end),-pk(1:N)],p,N).*InvF,p,N);
A = ModReduce(fqm(-S,2,N).*InvF,p,N);
B = ModReduce(fqm(msg,2,N).*InvF,p,N);
lhs = ModReduce(fqm(pk(1:N),2,N).*A + fqm(pk(N+1:end),2,N).*B, p, N);
rhs = fqm(qr(0,N-1),q,N).*ModReduce(InvF*S,p,N);
y = isequal(lhs, rhs);
end
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