Bleichenbacher's Attack (1998): The Original RSA Padding Oracle Vulnerability

Introduction

In 1998, Daniel Bleichenbacher published a groundbreaking paper that would go on to change the landscape of cryptography. His attack, now known as Bleichenbacher's attack, targeted the RSA cryptosystem when used with the PKCS #1 v1.5 padding scheme. This attack demonstrated the devastating consequences of subtle information leaks about padding validity, leading to a fundamental break in the confidentiality of a widely deployed cryptosystem.

Background

RSA is a widely used public-key cryptosystem, based on the difficulty of factoring large composite numbers. The RSA cryptosystem relies on the principle of modular arithmetic, where a plaintext message is encrypted by raising it to a certain power modulo a large composite number, known as the modulus. The modulus is typically the product of two large prime numbers, p and q.

PKCS #1 v1.5 Padding Scheme

The PKCS #1 v1.5 padding scheme was a widely used method for padding plaintext messages before encryption. The scheme involves appending a random number of bytes, known as the padding, to the plaintext message. The padding is designed to make the plaintext message a multiple of the block size of the encryption algorithm.

Bleichenbacher's Attack

Bleichenbacher's attack exploited a subtle information leak in the PKCS #1 v1.5 padding scheme. When a padding oracle is available, an attacker can use it to determine whether a given ciphertext is valid or not. A padding oracle is a function that takes a ciphertext as input and returns a boolean value indicating whether the ciphertext is valid or not.

The Attack

The attack works by iteratively modifying the ciphertext, using the padding oracle to determine whether the modified ciphertext is valid or not. The attacker starts by guessing a possible plaintext message, and then iteratively modifies the ciphertext to try to make it valid.

The Padding Oracle

The padding oracle is the key component of Bleichenbacher's attack. It is a function that takes a ciphertext as input and returns a boolean value indicating whether the ciphertext is valid or not. The padding oracle is typically implemented as part of a cryptographic library or a secure socket layer (SSL) implementation.

The Attack in Practice

To demonstrate the attack, let's consider an example. Suppose an attacker wants to recover the plaintext message "Hello, World!". They start by guessing a possible plaintext message, and then iteratively modify the ciphertext to try to make it valid.

ciphertext = 0x12345678...  # initial ciphertext
plaintext = "Hello, World!"  # guessed plaintext message

while True:
    # modify the ciphertext
    ciphertext = modify_ciphertext(ciphertext)

    # query the padding oracle
    if padding_oracle(ciphertext):
        # if the ciphertext is valid, try to recover the plaintext
        if recover_plaintext(ciphertext) == plaintext:
            print("Plaintext recovered!")
            break
    else:
        # if the ciphertext is not valid, try a different modification
        modify_ciphertext(ciphertext)

Security Implications

Bleichenbacher's attack demonstrated the devastating consequences of subtle information leaks about padding validity. The attack showed that even a small information leak about padding validity could be used to recover the plaintext message.

Best Practices

To prevent Bleichenbacher's attack, it is essential to use a padding scheme that is resistant to attacks. The PKCS #1 v2.1 padding scheme is a widely used alternative that is resistant to Bleichenbacher's attack.

Conclusion

Bleichenbacher's attack is a powerful reminder of the importance of cryptographic best practices. By understanding the risks associated with padding oracles, we can design more secure cryptographic protocols that are resistant to attacks.