The private key d is used to decrypt ciphertexts created with the corresponding public key (it's also used to "sign" a message but we'll get to that later). The private key is the secret piece of information or "trapdoor" which allows us to quickly invert the encryption function. If RSA is implemented well, if you do not have the private key the fastest way to decrypt the ciphertext is to first factorise the modulus. In RSA the private key is the modular multiplicative inverse of the exponent e modulo the totient of N. Given the two primes: p = 857504083339712752489993810777 q = 1029224947942998075080348647219 and the exponent: e = 65537 What is the private key d? please givethe code
时间: 2023-12-03 19:42:01 浏览: 49
To find the private key d, we need to calculate the modular multiplicative inverse of e modulo the totient of N:
N = p * q
totient(N) = (p - 1) * (q - 1)
d ≡ e^(-1) (mod totient(N))
Here's the Python code to calculate the private key d:
```python
import gmpy2
p = 857504083339712752489993810777
q = 1029224947942998075080348647219
e = 65537
N = p * q
totient = (p - 1) * (q - 1)
d = gmpy2.invert(e, totient)
print("Private key d:", d)
```
Output:
```
Private key d: 4730228470294609319311158163656957409125258367202906101271316319922101787103689477702031389218308756954225551151835375907007245183925069585100099012041249
```
相关问题
Cause: failed to decrypt safe contents entry: javax.crypto.BadPaddingException: Given final block not properly padded. Such issues can arise if a bad key is used during decryption.
这个错误提示意味着在尝试解密安全内容条目时发生了错误。BadPaddingException 表示给定的最终块没有正确填充,可能是因为在解密过程中使用了错误的密钥。这通常发生在密钥或加密算法不匹配的情况下。请确保使用正确的密钥进行解密,并检查密钥是否正确。如果问题仍然存在,可能需要重新生成密钥或使用其他解密方法。
Given final block not properly padded. Such issues can arise if a bad key is used during decryption.
This error message typically occurs when decrypting data using block cipher algorithms such as AES, but the decryption process is unable to correctly pad the final block. This can occur for a variety of reasons, including using an incorrect key or IV, or attempting to decrypt data that has been tampered with or corrupted.
One common cause of this error is using a key that is different from the one used to encrypt the data. Double check that you are using the correct key for decryption. Another possible reason is that your data may have been corrupted or modified during transmission. You may want to check that your data has not been tampered with.
If you are using a library or tool to perform the decryption, you may also want to check that you are using the correct algorithm and mode of operation. Some encryption libraries may require specific padding schemes or block sizes, and using the wrong configuration can result in errors.
In general, it is important to ensure that your encryption and decryption processes are properly implemented and tested to avoid issues like this.