signature shemes in python
- pure python without any external dependencies
- just copy and paste; no license; no installation
- simple implementation for understanding not for performance
- Specification: https://sphincs.org/data/sphincs+-r3.1-specification.pdf
- Reference Implementation: https://github.com/sphincs/sphincsplus
- Section 6. SPHINCS+
- If you have found a pair of input and output which is not equal to that of the reference implementaion, please let me know.
n = 16
algo = "shake"
robust = True
k = 14; a = 12
w = 4; h = 9; d = 7
pp = (n, algo, robust, k, a, w, h, d)
assert w in [4, 8]
secret_seed = b"\xaa"*n
public_seed = b"\xcc"*n
public_root = SPHINCS_GeneratePulicKey(pp, secret_seed, public_seed)
print(len(public_root), public_root.hex())
#16 9ab7a7b30bc9c6a8637a54caef3f9c27
rand = bytes.fromhex("a2fac94d6e320ad83fc049c6ba21033b")
msg = b"\xff"*32
signature = SPHINCS_Sign(pp, secret_seed, public_seed, public_root, msg, rand)
# Random: 16 a2fac94d6e320ad83fc049c6ba21033b
#Hashed Message: 6391030117691388 241 21 265dc48ab5c151e14d73ddc62ab3646a5e1474ca73
# FORS: 16 2f4db3d8172f2680e71f13e8b6dd3645
# XMSS-MT: tree_index leaf_index
# 0-th layer: 6391030117691388 241 => 16 85a91c6b80a1849f411d02ff73c1262a
# 1-th layer: 12482480698615 508 => 16 774a93c53745b203bc89c2ccedcc40bf
# 2-th layer: 24379845114 247 => 16 e698d35c86bc973a046f0cdbfed79bc1
# 3-th layer: 47616884 506 => 16 286c22499dca6d3a8cf0ba9ed9a8b5ed
# 4-th layer: 93001 372 => 16 ae3287acf595e9ef928f73484a60058e
# 5-th layer: 181 329 => 16 81b4e5c89d697835b45d23843b1f4e95
# 6-th layer: 0 181 => 16 9ab7a7b30bc9c6a8637a54caef3f9c27
root = SPHINCS_Verify(pp, public_seed, public_root, signature, msg)
assert root == public_root- Section 5. FORS: Forest Of Random Subsets
n = 16
algo = "shake"
robust = True
k = 14; a = 12
pp = (n, algo, robust, k, a)
secret_seed = b"\xaa"*n
#public_seed = b"\xbb"*n
public_seed = None
mt_addr = [0, 0, 0]
pk = FORS_GeneratePublicKey(pp, secret_seed, public_seed, mt_addr)
(public_seed, public_root) = pk
msg = b"Hello World!"
#rand = random.randbytes(n)
rand = None
signature = FORS_Sign(pp, sk, pk, msg, rand, mt_addr)
(rand, sigs) = signature
assert FORS_Verify(pp, pk, signature, msg, mt_addr)- Section 3. WOTS+ One-Time Signatures
n = 16
algo = "shake"
robust = True
w = 4
pp = (n, algo, robust, w)
secret_seed = b"\xaa"*n
#public_seed = b"\xbb"*n
public_seed = None
mt_addr = [0, 0, 0]
pk = WOTS_GeneratePublicKey(pp, secret_seed, public_seed, mt_addr)
(public_seed, public_root) = pk
msg = b"Hello World!"
#rand = random.randbytes(n)
rand = None
signature = WOTS_Sign(pp, sk, pk, msg, rand, mt_addr)
(rand, sigs) = signature
assert WOTS_Verify(pp, pk, signature, msg, mt_addr)- Section 4.1. (Fixed Input-Length) XMSS
- Section 4.2. HT: The Hypertee