Author(s): Bruce Schneier

ISBN: 0471128457

Publication Date: 01/01/96

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Here is a method to use 48 additional key bits to generate S-boxes that are resistant to both linear and differential cryptanalysis [165].

**(1)**Rearrange the DES S-boxes: 24673158.**(2)**Select 16 of the remaining key bits. If the first bit is 1, swap the first two rows of S-box 1 with the last two rows of S-box 1. If the second bit is a 1, swap the first eight columns of S-box 1 with the second eight columns of S-box 1. Do the same to S-box 2 with the third and fourth key bits. Do the same with S-boxes 3 through 8.**(3)**Take the remaining 32 key bits. XOR the first four with every entry of S-box 1, the second four with every entry of S-box 2 and so on.

The complexity of a differential cryptanalysis attack against this system is 2^{51}; the complexity of a linear cryptanalysis attack is 2^{53}. The complexity of exhaustive search is 2^{102}.

What is neat about this DES variant is that it can be implemented in existing hardware. Several DES chip vendors sell DES chips with loadable S-boxes. This S-box generation method can be done outside the chip and then loaded in. Differential and linear cryptanalysis require so much known or chosen plaintext as to be unworkable, and a brute-force attack is inconceivable—with no speed penalties.

The answer is both easy and hard. The easy answer just looks at key length (see Section 7.1). A brute-force DES-cracking machine that can find a key in an average of 3.5 hours cost only $1 million in 1993 [1597,1598]. DES is so widespread that it is na•ve to pretend that the NSA and its counterparts haven’t built such a machine. And remember that cost will drop by a factor of 5 every 10 years. DES will only become less secure as time goes on.

The hard answer tries to estimate cryptanalytic techniques. Differential cryptanalysis was known by the NSA long before the mid-1970s, when DES first became a standard. It is na•ve to pretend that the NSA theoreticians have been idle since then; almost certainly they have developed newer cryptanalytic techniques that can be applied against DES. But there are no facts, only rumors.

Winn Schwartau writes that the NSA had built a massively parallel DES-cracking machine as early as the mid-1980s [1404]. At least one such machine was built by Harris Corp. with a Cray Y-MP as a front end. Supposedly there are a series of algorithms that can reduce the complexity of a DES brute-force search by several orders of magnitude. Contextual algorithms, based on the inner workings of DES, can scrap sets of possible keys based on partial solutions. Statistical algorithms reduce the effective key size even further. And other algorithms choose likely keys—words, printable ASCII, and so on (see Section 8.1)—to test. The rumor is that the NSA can crack DES in 3 to 15 minutes, depending on how much preprocessing they can do. And these machines cost only $50,000 each, in quantity.

A different rumor is that if the NSA has a large amount of plaintext and ciphertext, its experts can perform some kind of statistical calculation and then go out to an array of optical disks and retrieve the key.

These are just rumors, but they don’t give me a warm, fuzzy feeling about DES. It has just been too big a target for too long. Almost any change to DES will be more annoying; maybe the resultant cipher will be easier to break, but the NSA might not have the resources to devote to the problem.

My recommendation is to use Biham’s construction for key-dependent S-boxes. It is easy to implement in software and in hardware chips that have loadable S-boxes, and has no performance penalty over DES. It increases the algorithm’s resistance to a brute-force attack, makes differential and linear cryptanalysis harder, and gives the NSA something at least as strong as DES—but different—to worry about.

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