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Publication# Breaking The FF3 Format-Preserving Encryption Standard Over Small Domains

Abstract

The National Institute of Standards and Technology (NIST) recently published a Format-Preserving Encryption standard accepting two Feistel structure based schemes called FF1 and FF3. Particularly, FF3 is a tweakable block cipher based on an 8-round Feistel network. In CCS~2016, Bellare et. al. gave an attack to break FF3 (and FF1) with time and data complexity $O(N^5\log(N))$, which is much larger than the code book (but using many tweaks), where $N^2$ is domain size to the Feistel network. In this work, we give a new practical total break attack to the FF3 scheme (also known as BPS scheme). Our FF3 attack requires $O(N^{\frac{11}{6}})$ chosen plaintexts with time complexity $O(N^{5})$. Our attack was successfully tested with $N\leq2^9$. It is a slide attack (using two tweaks) that exploits the bad domain separation of the FF3 design. Due to this weakness, we reduced the FF3 attack to an attack on 4-round Feistel network. Biryukov et. al. already gave a 4-round Feistel structure attack in SAC~2015. However, it works with chosen plaintexts and ciphertexts whereas we need a known-plaintext attack. Therefore, we developed a new generic known-plaintext attack to 4-round Feistel network that reconstructs the entire tables for all round functions. It works with $N^{\frac{3}{2}} \left( \frac{N}{2} \right)^{\frac{1}{6}}$ known plaintexts and time complexity $O(N^{3})$. Our 4-round attack is simple to extend to five and more rounds with complexity $N^{(r-5)N+o(N)}$. It shows that FF1 with $N=7$ and FF3 with $7\leq N\leq10$ do not offer a 128-bit security. Finally, we provide an easy and intuitive fix to prevent the FF3 scheme from our $O(N^{5})$ attack.

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Related publications (52)

Related concepts (39)

Format-preserving encryption

In cryptography, format-preserving encryption (FPE), refers to encrypting in such a way that the output (the ciphertext) is in the same format as the input (the plaintext). The meaning of "format" varies. Typically only finite sets of characters are used; numeric, alphabetic or alphanumeric. For example: Encrypting a 16-digit credit card number so that the ciphertext is another 16-digit number. Encrypting an English word so that the ciphertext is another English word.

Chosen-plaintext attack

A chosen-plaintext attack (CPA) is an attack model for cryptanalysis which presumes that the attacker can obtain the ciphertexts for arbitrary plaintexts. The goal of the attack is to gain information that reduces the security of the encryption scheme. Modern ciphers aim to provide semantic security, also known as ciphertext indistinguishability under chosen-plaintext attack, and they are therefore, by design, generally immune to chosen-plaintext attacks if correctly implemented.

Plaintext

In cryptography, plaintext usually means unencrypted information pending input into cryptographic algorithms, usually encryption algorithms. This usually refers to data that is transmitted or stored unencrypted. With the advent of computing, the term plaintext expanded beyond human-readable documents to mean any data, including binary files, in a form that can be viewed or used without requiring a key or other decryption device. Information—a message, document, file, etc.

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