FEAL-4 is breakable with 5 known plaintexts in 6 minutes.

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A New Method for Known Plaintext Attack on FEAL Cipher [98]

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The Fast d a t a Encryption ALgorithm, or FEAL, is a block cipher developed by Shimizu and Miyaguchi [134] and announced publicly in 1987. The original version of the algorithm, which is now known as FEAL-4, consists of four rounds, and it was designed t o be extremely efficient, with a modest degree of security. However, devastating attacks on FEAL-4 were soon discovered, rendering the algorithm insecure for virtually any conceivable application. The developers of FEAL responded by adding more rounds-first eight rounds (FEAL-8), then a variable number of rounds (FEAL-N)-and with a larger key (FEAL-NX). All versions of FEAL are insecure. Nevertheless, FEAL is an historically important cipher, since it spawned many developments in the field of cryptanalysis. In particular, Biham and Shamir's differential cryptanalysis [14] was specifically developed t o attack FEAL. Differential cryptanalysis was then furt,hered honed on the Data Encryption Standard (DES), and it was ultimately discovered that DES was designed t o resist such attacks. Apparently, differential cryptanalysis was known by someone involved in the development of DES (namely, the National Security Agency [140]) almost 20 years before it was, independently, rediscovered by Biham and Shamir, and it was considered it serious threat. In the next section, we consider the original and simplest version of FEAL, now known as FEAL-4. In Section 4.7.2 we present a differential attack that can recover the 64-bit key with a work factor of about 2'' and only requires four pairs of chosen plaintext blocks. Similar attacks succeed against FEAL-8 (and other versions of FEAL), but the work factor is higher and the implementations are more complex. In Section 4.7.3 we discuss the linear cryptanalysis of FEAL-4. Linear cryptanalysis was invented by Matsui [97], originally as a way t o attack DES. Linear cryptanalysis is also highly effective against FEAL-4. Today, linear and differential cryptanalysis are standard tools used t o analyze all block cipher designs. These powerful techniques can be used t o probe for potential weaknesses. However, neither technique is generally useful

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4.7 FEAL

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for practical attacks on ciphers. Partly, this is due to the fact that modern block ciphers are designed with linear and differential attacks in mind, but it is also due to the fact that these attacks are inherently impractical. The primary reason for the impracticality of differential and linear cryptanalysis is that they require large amounts of chosen plaintext (differential cryptanalysis) or known plaintext (linear cryptanalysis). For example, practical attacks against DES invariably rely on an exhaustive key search to recover the 56-bit key, even though linear cryptanalytic attacks with significantly lower work factors are known. It is simply more effective in practice to pay the price of a higher work factor rather than to deal with the huge volumes of data required by these advanced cryptanalytic techniques. Also, it would generally be impractical to expect to collect huge amounts of known (or chosen) plaintext. In this regard, FEAL is an exceptional block cipher, since practical linear and differential attacks are possible. Nevertheless, even for FEAL-4, linear and differential attacks are not trivial, and considerable care is required to actually implement these attacks to recover the key.

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FEAL-4 Cipher

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There are several equivalent descriptions of the FEAL-4 cipher. In this section, we present a description that is suited for differential and linear attacks; see Problem 27 for the original description of FEAL-4. FEAL-4 is a four-round Feistel Cipher with a block size of 64 bits and a 64-bit key [134]. In our description of the cipher, the key is expanded into six 32-bit subkeys (the original description uses twelve 16-bit subkeys). Our version of FEAL-4 appears in Figure 4.16. We ignore the key schedule algorithm, which is used to derive the subkeys from the 64-bit key, since the attacks discussed here will directly recover the subkeys. Once the subkeys have been recovered, it is straightforward to recover the original key, see [14] for the details. The FEAL round function F is illustrated in Figure 4.17. The 32-bit input to F consists of the four bytes (zg,z1,z~,zg) the 32-bit output is and given by the four bytes (yo, y1, ~ 2y3). The functions Go and GI each take two , bytes of input and each generates a single byte of output. These functions are defined as (4.24) Go(a,b) = (a b (mod 256)) << 2 <

G I ( ub ) = ( u ,

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