由X-Cube Crypto Library(Embedded C)生成的RSA签名和Python脚本不匹配,即使我们为这两种方法使用了相同的密钥

3z6pesqy  于 2023-06-21  发布在  Python
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我的应用程序生成SHA 256哈希值的“xx_xx.hex”文件,然后生成RSA签名的哈希。X-Cube-CRYPTOLIB和python脚本生成的SHA 256值相同。但是RSA签名是不一样的。
我使用openssl创建了1024个密钥对,哈希值由X-Cube生成-CRYPTOLIB是十进制格式,但它相当于python脚本生成的哈希值(十六进制格式)。
生成的SHA 256值为:5b4c333945c47a952bfe1571e5b58b4674985fa754f19abcb5739f4c2dda433b
但是X-Cube-CRYPTOLIB十进制值生成的签名不等同于python脚本生成的签名(十六进制格式)。
下面是python脚本的结果;
十六进制签名:72869266541a76bc2a73437e53c1c917e4b2dd323f8b9735e44f6d600e7fe414c0899e41e0a89c557bcd3673dac2084409fabb0ef52574108363fdd3bdc44d2239371fe3e0617966f93964db42d12ad91b254b70af7add8cd1043d7f6a5857ea834c885480d5ac2 d792c514233fcc62eea3149fc8fa50e0e2579f780ff6e1c37
请找到下面的图像来检查由X-Cube-CRYPTOLIB生成的签名,它是不完整的。但仅供参考,我们可以看到几个字节。computed singature X-Cube-CRYPTOLIB
Python脚本:

import hashlib
import sys
from intelhex import IntelHex
from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.asymmetric import padding, rsa
from cryptography.hazmat.backends import default_backend
from cryptography.hazmat.primitives import serialization
import os
import binascii

 
# Path to the hex file you want to load
file_path  = 'W:/xxx/xxx/xxx_input.hex'
privkey_path = 'W:/xxx/xxx/rivate_1024key.pem'
pubkey_path = 'W:/xxx/xxx/public_1024key.pem'
output_file = 'W:/xxx/xxx//Hash.txt'
outhex_file = 'W:/xxx/xxx/xxx_output.hex'

# Define the ranges() function
def ranges(addresses):
    start = addresses[0]
    end = addresses[0]
    for address in addresses[1:]:
        if address == end + 1:
            end = address
        else:
            yield start, end
            start = address
            end = address
    yield start, end

# Load the Intel Hex file
hex = IntelHex(file_path)

# Get the sorted list of addresses
addresses = hex.addresses()
addresses.sort()

# Iterate over address ranges and extract the data
data_list = list(ranges(addresses))
for start, end in data_list:
    size = end - start + 1
    data = list(hex.tobinarray(start=start, size=size)) 
    # Convert the data to hexadecimal format
    hex_data = ''.join(format(byte, '02x') for byte in data)  
    data_bytes = bytes.fromhex(hex_data)
    hasher = hashlib.sha256()
    hasher.update(data_bytes)
    hash_value = hasher.hexdigest()
    # Print the hash value in hexadecimal format
    print("SHA256 Hash Value:", hash_value)
    # Digest to be signed
    # Convert the hash value to bytes
    digest_bytes = bytes.fromhex(hash_value)

   
    # Load the private key from file
try:
    with open(privkey_path, 'rb') as f:
        private_key = serialization.load_pem_private_key(
        f.read(),
        password=None,
        backend=default_backend()
    )
    print("private_key:", private_key)
    # If no exception occurred, the private key was loaded successfully
    print("Private key loaded successfully.")

    # Use the private key for signing or other operations
    
except Exception as e:
    print("Error loading private key:", e)

# Save the digest bytes to a file
with open(output_file, 'wb') as file:
    file.write(digest_bytes)
    print("Digest:", digest_bytes)

# Sign the digest with the private key
signature = private_key.sign(
    digest_bytes,
    padding.PKCS1v15(),  # Use PKCS1v15 padding scheme for RSA signatures
    hashes.SHA256()  # Use SHA256 hashing algorithm
)

# Convert the signature to hexadecimal format if needed
hex_signature = signature.hex()

# Print the hexadecimal signature
print("Hexadecimal signature:", hex_signature)

X-Cube的C代码:

const uint8_t Message[] =
{
  0xcd, 0xc8, 0x7d, 0xa2, 0x23, 0xd7, 0x86, 0xdf, 0x3b, 0x45, 0xe0, 0xbb, 0xbc, 0x72, 0x13, 0x26,
  0xd1, 0xee, 0x2a, 0xf8, 0x06, 0xcc, 0x31, 0x54, 0x75, 0xcc, 0x6f, 0x0d, 0x9c, 0x66, 0xe1, 0xb6,
  0x23, 0x71, 0xd4, 0x5c, 0xe2, 0x39, 0x2e, 0x1a, 0xc9, 0x28, 0x44, 0xc3, 0x10, 0x10, 0x2f, 0x15,
  0x6a, 0x0d, 0x8d, 0x52, 0xc1, 0xf4, 0xc4, 0x0b, 0xa3, 0xaa, 0x65, 0x09, 0x57, 0x86, 0xcb, 0x76,
  0x97, 0x57, 0xa6, 0x56, 0x3b, 0xa9, 0x58, 0xfe, 0xd0, 0xbc, 0xc9, 0x84, 0xe8, 0xb5, 0x17, 0xa3,
  0xd5, 0xf5, 0x15, 0xb2, 0x3b, 0x8a, 0x41, 0xe7, 0x4a, 0xa8, 0x67, 0x69, 0x3f, 0x90, 0xdf, 0xb0,
  0x61, 0xa6, 0xe8, 0x6d, 0xfa, 0xae, 0xe6, 0x44, 0x72, 0xc0, 0x0e, 0x5f, 0x20, 0x94, 0x57, 0x29,
  0xcb, 0xeb, 0xe7, 0x7f, 0x06, 0xce, 0x78, 0xe0, 0x8f, 0x40, 0x98, 0xfb, 0xa4, 0x1f, 0x9d, 0x61,
  0x93, 0xc0, 0x31, 0x7e, 0x8b, 0x60, 0xd4, 0xb6, 0x08, 0x4a, 0xcb, 0x42, 0xd2, 0x9e, 0x38, 0x08,
  0xa3, 0xbc, 0x37, 0x2d, 0x85, 0xe3, 0x31, 0x17, 0x0f, 0xcb, 0xf7, 0xcc, 0x72, 0xd0, 0xb7, 0x1c,
  0x29, 0x66, 0x48, 0xb3, 0xa4, 0xd1, 0x0f, 0x41, 0x62, 0x95, 0xd0, 0x80, 0x7a, 0xa6, 0x25, 0xca,
  0xb2, 0x74, 0x4f, 0xd9, 0xea, 0x8f, 0xd2, 0x23, 0xc4, 0x25, 0x37, 0x02, 0x98, 0x28, 0xbd, 0x16,
  0xbe, 0x02, 0x54, 0x6f, 0x13, 0x0f, 0xd2, 0xe3, 0x3b, 0x93, 0x6d, 0x26, 0x76, 0xe0, 0x8a, 0xed,
  0x1b, 0x73, 0x31, 0x8b, 0x75, 0x0a, 0x01, 0x67, 0xd0
};
const uint8_t Known_Signature[] =
{
  0x6b, 0xc3, 0xa0, 0x66, 0x56, 0x84, 0x29, 0x30, 0xa2, 0x47, 0xe3, 0x0d, 0x58, 0x64, 0xb4, 0xd8,
  0x19, 0x23, 0x6b, 0xa7, 0xc6, 0x89, 0x65, 0x86, 0x2a, 0xd7, 0xdb, 0xc4, 0xe2, 0x4a, 0xf2, 0x8e,
  0x86, 0xbb, 0x53, 0x1f, 0x03, 0x35, 0x8b, 0xe5, 0xfb, 0x74, 0x77, 0x7c, 0x60, 0x86, 0xf8, 0x50,
  0xca, 0xef, 0x89, 0x3f, 0x0d, 0x6f, 0xcc, 0x2d, 0x0c, 0x91, 0xec, 0x01, 0x36, 0x93, 0xb4, 0xea,
  0x00, 0xb8, 0x0c, 0xd4, 0x9a, 0xac, 0x4e, 0xcb, 0x5f, 0x89, 0x11, 0xaf, 0xe5, 0x39, 0xad, 0xa4,
  0xa8, 0xf3, 0x82, 0x3d, 0x1d, 0x13, 0xe4, 0x72, 0xd1, 0x49, 0x05, 0x47, 0xc6, 0x59, 0xc7, 0x61,
  0x7f, 0x3d, 0x24, 0x08, 0x7d, 0xdb, 0x6f, 0x2b, 0x72, 0x09, 0x61, 0x67, 0xfc, 0x09, 0x7c, 0xab,
  0x18, 0xe9, 0xa4, 0x58, 0xfc, 0xb6, 0x34, 0xcd, 0xce, 0x8e, 0xe3, 0x58, 0x94, 0xc4, 0x84, 0xd7
};

const uint8_t Modulus[] =
{
  0xa5, 0x6e, 0x4a, 0x0e, 0x70, 0x10, 0x17, 0x58, 0x9a, 0x51, 0x87, 0xdc, 0x7e, 0xa8, 0x41, 0xd1,
  0x56, 0xf2, 0xec, 0x0e, 0x36, 0xad, 0x52, 0xa4, 0x4d, 0xfe, 0xb1, 0xe6, 0x1f, 0x7a, 0xd9, 0x91,
  0xd8, 0xc5, 0x10, 0x56, 0xff, 0xed, 0xb1, 0x62, 0xb4, 0xc0, 0xf2, 0x83, 0xa1, 0x2a, 0x88, 0xa3,
  0x94, 0xdf, 0xf5, 0x26, 0xab, 0x72, 0x91, 0xcb, 0xb3, 0x07, 0xce, 0xab, 0xfc, 0xe0, 0xb1, 0xdf,
  0xd5, 0xcd, 0x95, 0x08, 0x09, 0x6d, 0x5b, 0x2b, 0x8b, 0x6d, 0xf5, 0xd6, 0x71, 0xef, 0x63, 0x77,
  0xc0, 0x92, 0x1c, 0xb2, 0x3c, 0x27, 0x0a, 0x70, 0xe2, 0x59, 0x8e, 0x6f, 0xf8, 0x9d, 0x19, 0xf1,
  0x05, 0xac, 0xc2, 0xd3, 0xf0, 0xcb, 0x35, 0xf2, 0x92, 0x80, 0xe1, 0x38, 0x6b, 0x6f, 0x64, 0xc4,
  0xef, 0x22, 0xe1, 0xe1, 0xf2, 0x0d, 0x0c, 0xe8, 0xcf, 0xfb, 0x22, 0x49, 0xbd, 0x9a, 0x21, 0x37
};
const uint8_t Public_Exponent[] =
{
  0x01, 0x00, 0x01
};
const uint8_t Private_Exponent[] =
{
  0x33, 0xa5, 0x04, 0x2a, 0x90, 0xb2, 0x7d, 0x4f, 0x54, 0x51, 0xca, 0x9b, 0xbb, 0xd0, 0xb4, 0x47,.......};
const uint8_t P_Prime[] =
{
  0xe7, 0xe8, 0x94, 0x27, 0x20, 0xa8, 0x77, 0x51, 0x72, 0x73, 0xa3, 0x56, 0x05, 0x3e, 0xa2, 0xa1,....};
const uint8_t Q_Prime[] =
{
  0xb6, 0x9d, 0xca, 0x1c, 0xf7, 0xd4, 0xd7, 0xec, 0x81, 0xe7, 0x5b, 0x90, 0xfc, 0xca, 0x87, 0x4a, ..........};
const uint8_t P_Prime_Exponent[] =
{
  0x28, 0xfa, 0x13, 0x93, 0x86, 0x55, 0xbe, 0x1f, 0x8a, 0x15, 0x9c, 0xba, 0xca, 0x5a, 0x72, 0xea,.............};
const uint8_t Q_Prime_Exponent[] =
{
  0x1a, 0x8b, 0x38, 0xf3, 0x98, 0xfa, 0x71, 0x20, 0x49, 0x89, 0x8d, 0x7f, 0xb7, 0x9e, 0xe0, 0xa7,....};
const uint8_t Coefficient[] =
{
  0x27, 0x15, 0x6a, 0xba, 0x41, 0x26, 0xd2, 0x4a, 0x81, 0xf3, 0xa5, 0x28, 0xcb, 0xfb, 0x27, 0xf5,... };

    uint8_t Computed_Signature[128];

    uint8_t computed_hash[CMOX_SHA256_SIZE];

    const uint8_t Public_Exponent[] = {0x01, 0x00, 0x01};

    uint8_t Working_Buffer[3500];

    StartAddress = 0x0802A000;
    EndAddress = 0x0802FF00;

    /* Compute directly the digest passing all the needed parameters */
hretval = cmox_hash_compute(CMOX_SHA256_ALGO, /* Use SHA256 algorithm */
                            const uint8_t*)(uintptr_t)StartAddress,
                            (EndAddress - StartAddress + 1), /* Message to digest */
                             computed_hash,    /* Data buffer to receive digest data */
                             CMOX_SHA256_SIZE, /* Expected digest size */
                             &computed_size);  /* Size of computed digest *

/* Construct a RSA context, specifying mathematics implementation and working buffer for later processing */
cmox_rsa_construct(&Rsa_Ctx, CMOX_RSA_MATH_FUNCS, CMOX_MODEXP_PRIVATE, Working_Buffer, sizeof(Working_Buffer));

retval = cmox_rsa_setKeyCRTwithFACM(&Rsa_Key,                                   /* RSA key structure to fill */
                                    sizeof(Modulus) * 8,                        /* Private key modulus bit length */
                                    P_Prime_Exponent, sizeof(P_Prime_Exponent), /* P prime */
                                    Q_Prime_Exponent, sizeof(Q_Prime_Exponent), /* Q prime */
                                    P_Prime, sizeof(P_Prime),                   /* P prime exponent */
                                    Q_Prime, sizeof(Q_Prime),                   /* Q prime exponent */
                                    Coefficient, sizeof(Coefficient),           /* Coefficient */
                                    Public_Exponent, sizeof(Public_Exponent));  /* Public exponent */

/* Compute directly the signature passing all the needed parameters */
retval = cmox_rsa_pkcs1v15_sign(&Rsa_Ctx,                            /* RSA context */
                                &Rsa_Key,                            /* RSA key to use */
                                computed_hash,                       /* Digest to sign */
                                CMOX_RSA_PKCS1V15_HASH_SHA256,       /* Method used to compute the digest */
                                Computed_Signature, &computed_size); /* Data buffer to receive signature */

在脚本中,我使用PKCS 1v 15填充方案进行RSA签名,这与C代码类似。但签名还是不一样。
请指出这里的错误是什么。可能是任何数据格式转换或双散列或其他东西?

yhqotfr8

yhqotfr81#

当使用公钥解密签名而不移除填充时:

signature = bytes.fromhex("6bc3a06656842930a247e30d5864b4d819236ba7c68965862ad7dbc4e24af28e86bb531f03358be5fb74777c6086f850caef893f0d6fcc2d0c91ec013693b4ea00b80cd49aac4ecb5f8911afe539ada4a8f3823d1d13e472d1490547c659c7617f3d24087ddb6f2b72096167fc097cab18e9a458fcb634cdce8ee35894c484d7")

modulus = bytes.fromhex("a56e4a0e701017589a5187dc7ea841d156f2ec0e36ad52a44dfeb1e61f7ad991d8c51056ffedb162b4c0f283a12a88a394dff526ab7291cbb307ceabfce0b1dfd5cd9508096d5b2b8b6df5d671ef6377c0921cb23c270a70e2598e6ff89d19f105acc2d3f0cb35f29280e1386b6f64c4ef22e1e1f20d0ce8cffb2249bd9a2137")
public_exponent = bytes.fromhex("010001")

signature_int = int.from_bytes(signature, 'big')
modulus_int = int.from_bytes(modulus, 'big')
public_exponent_int = int.from_bytes(public_exponent, 'big')
decrypted_int = pow(signature_int, public_exponent_int, modulus_int)
decrypted = decrypted_int.to_bytes(128, 'big')
print(decrypted.hex()) # 0001ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff003021300906052b0e03021a05000414cd8b6538cb8e8de566b68bd067569dbf1ee2718e

有效PKCS#1 v1.5签名结果:

0001ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff003021300906052b0e03021a05000414cd8b6538cb8e8de566b68bd067569dbf1ee2718e

的第一部分

3021300906052b0e03021a05000414 cd8b6538cb8e8de566b68bd067569dbf1ee2718e

由所使用的摘要的ID组成,并将SHA-1标识为应用的摘要(参见此处)。当生成所用数据的SHA-1哈希值时:

import hashlib
message = bytes.fromhex("cdc87da223d786df3b45e0bbbc721326d1ee2af806cc315475cc6f0d9c66e1b62371d45ce2392e1ac92844c310102f156a0d8d52c1f4c40ba3aa65095786cb769757a6563ba958fed0bcc984e8b517a3d5f515b23b8a41e74aa867693f90dfb061a6e86dfaaee64472c00e5f20945729cbebe77f06ce78e08f4098fba41f9d6193c0317e8b60d4b6084acb42d29e3808a3bc372d85e331170fcbf7cc72d0b71c296648b3a4d10f416295d0807aa625cab2744fd9ea8fd223c42537029828bd16be02546f130fd2e33b936d2676e08aed1b73318b750a0167d0")
hash = hashlib.sha1(message).hexdigest()
print(hash) # cd8b6538cb8e8de566b68bd067569dbf1ee2718e

散列是

cd8b6538cb8e8de566b68bd067569dbf1ee2718e

其对应于第二部分并且因此是一致的。
这表明X Cube代码使用SHA-1(而不是 * SHA-256)对数据进行散列,并使用RSA PKCS#1 v1.5对散列进行签名(因此 * 原始 * 数据的 * 单个 * 散列),即Python的对应部分可以实现如下:

from cryptography.hazmat.primitives import hashes
from cryptography.hazmat.primitives.asymmetric import padding
from cryptography.hazmat.primitives import serialization

# import private key (PEM key generated from the posted RSA parameters)
pkcs8pem = b'''-----BEGIN PRIVATE KEY-----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-----END PRIVATE KEY-----'''
private_key = serialization.load_pem_private_key(pkcs8pem, password=None)

# sign with RSA PKCS#1 v1.5 padding and SHA-1
message = bytes.fromhex("cdc87da223d786df3b45e0bbbc721326d1ee2af806cc315475cc6f0d9c66e1b62371d45ce2392e1ac92844c310102f156a0d8d52c1f4c40ba3aa65095786cb769757a6563ba958fed0bcc984e8b517a3d5f515b23b8a41e74aa867693f90dfb061a6e86dfaaee64472c00e5f20945729cbebe77f06ce78e08f4098fba41f9d6193c0317e8b60d4b6084acb42d29e3808a3bc372d85e331170fcbf7cc72d0b71c296648b3a4d10f416295d0807aa625cab2744fd9ea8fd223c42537029828bd16be02546f130fd2e33b936d2676e08aed1b73318b750a0167d0")
signature = private_key.sign(
    message,
    padding.PKCS1v15(),
    hashes.SHA1()
)

print(signature.hex()) # 6bc3a06656842930a247e30d5864b4d819236ba7c68965862ad7dbc4e24af28e86bb531f03358be5fb74777c6086f850caef893f0d6fcc2d0c91ec013693b4ea00b80cd49aac4ecb5f8911afe539ada4a8f3823d1d13e472d1490547c659c7617f3d24087ddb6f2b72096167fc097cab18e9a458fcb634cdce8ee35894c484d7

它提供了预期的签名:

6bc3a06656842930a247e30d5864b4d819236ba7c68965862ad7dbc4e24af28e86bb531f03358be5fb74777c6086f850caef893f0d6fcc2d0c91ec013693b4ea00b80cd49aac4ecb5f8911afe539ada4a8f3823d1d13e472d1490547c659c7617f3d24087ddb6f2b72096167fc097cab18e9a458fcb634cdce8ee35894c484d7

**编辑:**关于您的评论:

要传递散列消息而不是消息并禁用隐式散列,必须使用Prehashed。这里):

from cryptography.hazmat.primitives.asymmetric import utils
...
# sign with RSA PKCS#1 v1.5 padding and SHA-1 (pass message_hash, disable implicit hashing)
signature = private_key.sign(
    message_hash,
    padding.PKCS1v15(),
    utils.Prehashed(hashes.SHA1()) # apply Prehashed
)

其中,message_hash是作为字节类对象的消息的散列,例如,如下:

message = bytes.fromhex("cdc87da223d786df3b45e0bbbc721326d1ee2af806cc315475cc6f0d9c66e1b62371d45ce2392e1ac92844c310102f156a0d8d52c1f4c40ba3aa65095786cb769757a6563ba958fed0bcc984e8b517a3d5f515b23b8a41e74aa867693f90dfb061a6e86dfaaee64472c00e5f20945729cbebe77f06ce78e08f4098fba41f9d6193c0317e8b60d4b6084acb42d29e3808a3bc372d85e331170fcbf7cc72d0b71c296648b3a4d10f416295d0807aa625cab2744fd9ea8fd223c42537029828bd16be02546f130fd2e33b936d2676e08aed1b73318b750a0167d0")
digest = hashes.Hash(hashes.SHA1())
digest.update(message)
message_hash = digest.finalize()

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