Exercises: RSA Encrypt / Decrypt

In this exercise you shall encrypt and decrypt messages using the RSA public-key cryptosystem.

Encrypt Message with RSA-OAEP

You are given a text message and a RSA public key (in PEM format). Write a program to encrypt the message, using the RSA-OAEP encryption scheme (RSA + PKCS#1 OAEP padding).

Input:

  • First line: the input message

  • Next few lines: the RSA public key (in the PKCS#8 PEM ASN.1 format)

  • The public key length can be 512 bits, 1024 bits, 2048 bits, 3072 bits or 4096 bits.

Output:

  • The encrypted message, printed as hex string.

Write your code in programming language of choice.

Sample input:

Secret message
-----BEGIN PUBLIC KEY-----
MFwwDQYJKoZIhvcNAQEBBQADSwAwSAJBAMYhCcGpfoebriBbFaUMMwH3B5t7udir
ODJehnQTPlWLf9SVfQdx0v9ATJ2Rs5kQjdJ/wZYunMBVq6/FhgPZexsCAwEAAQ==
-----END PUBLIC KEY-----

The above input uses a 512-bit RSA public key and a small plain text message, that can fit inside the key length (after the OAEP padding).

Sample output (for the above input):

Note: the above output should be different at each execution due to the randomness injected by the OAEP padding algorithm.

Decrypt a Message with RSA-OAEP

You are given a RSA-OAEP-encrypted ciphertext (as hex string) and a RSA private key (in PEM format). Write a program to decrypt the message, using the RSA-OAEP encryption scheme (RSA + PKCS#1 OAEP padding).

Input:

  • First line: the ciphertext (the encrypted message), given as hex string

  • Next few lines: the RSA private key (in the PKCS#8 PEM ASN.1 format)

Output:

  • Print the decrypted message as plain text

  • Print Decryption failed! in case of problem

Write your code in programming language of choice.

Sample input:

The above input uses a 512-bit RSA private key and an encrypted ciphertext of the same length.

Sample output (for the above input):

Another sample input (wrong 512-bit private key):

The corresponding output should be:

Note that the RSA-OAEP padding algorithm has built-in checksum, which allows to detect incorrect decryption attempts, but it is not an authenticated encryption scheme.

* Implement Hybrid Encryption / Decryption with RSA-KEM

Write a program to encrypt a large message (bigger than the RSA key length, e.g. a PDF document) using the RSA-KEM hybrid encryption scheme with AES symmetric encryption (use block mode of choice, e.g. GCM or CTR).

Hint:

  • Check this example first: https://github.com/digitalbazaar/forge#rsakem.

  • Note that in some languages it is hard to find and RSA-KEM implementation, so you can skip this exercise or use another hybrid encryption scheme (e.g. RSA + AES + HMAC).

Input:

  • The message for encryption

  • RSA public key (in PEM format)

Output:

  • The encrypted ciphertext (hex string)

  • The random IV salt for the AES cipher (hex string)

  • The authentication tag / MAC for the encrypted message (hex string)

  • The encapsulated secret key for the AES algorithm (hex string)

Write a program to decrypt given encrypted message, produced by the previous exercise, using the RSA-KEM hybrid encryption scheme with AES symmetric encryption (use block mode of choice, e.g. GCM or CTR).

Input:

  • The encrypted ciphertext (hex string)

  • The random IV salt for the AES cipher (hex string)

  • The authentication tag / MAC for the encrypted message (hex string)

  • The encapsulated secret key for the AES algorithm (hex string)

Output:

  • The decrypted original plaintext message

  • Print Decryption failed! if the message decryption is not successful (e.g. wrong password)

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