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Cryptanalysis


Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key. In non-technical language, this is the practice of codebreaking or cracking the code, although these phrases also have a specialized technical meaning.

"Cryptanalysis" is also used to refer to any attempt to circumvent the security of other types of cryptographic algorithms and protocols in general, and not just encryption. However, cryptanalysis usually excludes methods of attack that do not primarily target weaknesses in the actual cryptography, such as bribery, physical coercion, burglary, keystroke logging, and social engineering, although these types of attack are an important concern and are often more effective than traditional cryptanalysis.

Even though the goal has been the same, the methods and techniques of cryptanalysis have changed drastically through the history of cryptography, adapting to increasing cryptographic complexity, ranging from the pen-and-paper methods of the past, through machines like Bombes and Colossus computers in World War II, to the computer-based schemes of the present. The results of cryptanalysis have also changed — it is no longer possible to have unlimited success in codebreaking, and there is a hierarchical classification of what constitutes an attack. In the mid-1970s, a new class of cryptography was introduced: asymmetric cryptography. Methods for breaking these cryptosystems are typically radically different from before, and usually involve solving carefully constructed problems in pure mathematics, the best-known being integer factorization.

History of cryptography

Cryptanalysis has coevolved together with cryptography, and the contest can be traced through the history of cryptography—new ciphers being designed to replace old broken designs, and new cryptanalytic techniques invented to crack the improved schemes. In practice, they are viewed as two sides of the same coin: in order to create secure cryptography, you have to design against possible cryptanalysis.

Classical cryptanalysis

First page of Al-Kindi's 9th century Manuscript on Deciphering Cryptographic Messages

Although the actual word "cryptanalysis" is relatively recent (it was coined by William Friedman in 1920), methods for breaking codes and ciphers are much older. The first known recorded explanation of cryptanalysis was given by 9th-century Arabian polymath, Al-Kindi (also known as "Alkindus" in Europe), in A Manuscript on Deciphering Cryptographic Messages. This treatise includes a description of the method of frequency analysis (Ibrahim Al-Kadi, 1992- ref-3). Italian scholar Giambattista della Porta was author of a seminal work on cryptanalysis "De Furtivis Literarum Notis".

Frequency analysis is the basic tool for breaking most classical ciphers. In natural languages, certain letters of the alphabet appear more frequently than others; in English, "E" is likely to be the most common letter in any sample of plaintext. Similarly, the digraph "TH" is the most likely pair of letters in English, and so on. Frequency analysis relies on a cipher failing to hide these statistics. For example, in a simple substitution cipher (where each letter is simply replaced with another), the most frequent letter in the ciphertext would be a likely candidate for "E". Frequency analysis of such a cipher is therefore relatively easy, provided that the ciphertext is long enough to give a reasonably representative count of the letters of the alphabet that it contains.

In Europe during the 15th and 16th centuries, the idea of a polyalphabetic substitution cipher was developed, among others by the French diplomat Blaise de Vigenère (1523–96). For some three centuries, the Vigenère cipher, which uses a repeating key to select different encryption alphabets in rotation, was considered to be completely secure (le chiffre indéchiffrable—"the indecipherable cipher"). Nevertheless, Charles Babbage (1791–1871) and later, independently, Friedrich Kasiski (1805–81) succeeded in breaking this cipher.[4] During World War I, inventors in several countries developed rotor cipher machines such as Arthur Scherbius' Enigma, in an attempt to minimize the repetition that had been exploited to break the Vigenère system.

In practice, frequency analysis relies as much on linguistic knowledge as it does on statistics, but as ciphers became more complex, mathematics became more important in cryptanalysis. This change was particularly evident before and during World War II, where efforts to crack Axis ciphers required new levels of mathematical sophistication. Moreover, automation was first applied to cryptanalysis in that era with the Polish Bomba device, the British Bombe development of it, the use of punched card equipment, and in the Colossus computers — the first electronic digital computers to be controlled by a program.

Depth

Sending two or more messages with the same key is an insecure process. To a cryptanalyst the messages are then said to be "in depth". This may be detected by the messages having the same indicator by which the sending operator informs the receiving operator about the key generator initial settings for the message. In a symmetrical cipher, the same key that was applied to the plaintext to produce the ciphertext is applied to the ciphertext to recover the plaintext. A simple example of such a system is the Vernam cipher in which a long key is bit-for-bit combined with the plaintext or ciphertext using the "XOR" operator (symbolized by \oplus):

    Plaintext \oplus Key = Ciphertext    at each bit position

and

    Ciphertext \oplus Key = Plaintext    at each bit position

When the ciphertexts are in depth, combining them eliminates the common key, leaving just a combination of the two plaintexts:

    Ciphertext1 \oplus Ciphertext2 = \alpha = Plaintext1\oplus Plaintext2    at each bit position

The individual plaintexts can then be worked out by trying probable words (or phrases) at various locations; when the corresponding section of α is XORed with a correct guess at the probable word, a stretch of the other plaintext is revealed, which can be recognized and (quite often) extended at each end, working back and forth between the plaintexts to recover much or all of them. When a recovered plaintext is then combined with its ciphertext, the key is revealed:

    Plaintext1 \oplus Ciphertext1 = Key    at each bit position

Knowledge of keys from a cipher may allow cryptanalysts to work out the system used for constructing them.

Depth reading can be applied in more complicated contexts to eliminate some of a system's parameters, or to "stack" messages so that source language statistics become exploitable. One way to properly align multiple messages that use the same periodic key starting at different positions is by the kappa test.

Modern cryptanalysis

The Bombe replicated the action of several Enigma machines wired together. Each of the rapidly rotating drums, pictured above in a Bletchley Park museum mockup, simulated the action of an Enigma rotor.

Even though computation was used to great effect in cryptanalysis of the Enigma and other systems during World War II, it also made possible new methods of cryptography orders of magnitude more complex than ever before. Taken as a whole, modern cryptography has become much more impervious to cryptanalysis than the pen-and-paper systems of the past, and now seems to have the upper hand against pure cryptanalysis. The historian David Kahn notes,

    "Many are the cryptosystems offered by the hundreds of commercial vendors today that cannot be broken by any known methods of cryptanalysis. Indeed, in such systems even a chosen plaintext attack, in which a selected plaintext is matched against its ciphertext, cannot yield the key that unlock[s] other messages. In a sense, then, cryptanalysis is dead. But that is not the end of the story. Cryptanalysis may be dead, but there is - to mix my metaphors - more than one way to skin a cat.".

Kahn goes on to mention increased opportunities for interception, bugging, side channel attacks, and quantum computers as replacements for the traditional means of cryptanalysis. In 2010, former NSA technical director Brian Snow said that both academic and government cryptographers are "moving very slowly forward in a mature field."

However, any postmortems for cryptanalysis may be premature. While the effectiveness of cryptanalytic methods employed by intelligence agencies remains unknown, many serious attacks against both academic and practical cryptographic primitives have been published in the modern era of computer cryptography:

    The block cipher Madryga, proposed in 1984 but not widely used, was found to be susceptible to ciphertext-only attacks in 1998.
    FEAL-4, proposed as a replacement for the DES standard encryption algorithm but not widely used, was demolished by a spate of attacks from the academic community, many of which are entirely practical.
    The A5/1, A5/2, CMEA, and DECT systems used in mobile and wireless phone technology can all be broken in hours, minutes or even in real-time using widely-available computing equipment.
    Brute-force keyspace search has broken some real-world ciphers and applications, including single-DES (see EFF DES cracker), 40-bit "export-strength" cryptography, and the DVD Content Scrambling System.
    In 2001, Wired Equivalent Privacy (WEP), a protocol used to secure Wi-Fi wireless networks, was shown to be breakable in practice because of a weakness in the RC4 cipher and aspects of the WEP design that made related-key attacks practical. WEP was later replaced by Wi-Fi Protected Access.
    In 2008, researchers conducted a proof-of-concept break of SSL using weaknesses in the MD5 hash function and certificate issuer practices that made it possible to exploit collision attacks on hash functions. The certificate issuers involved changed their practices to prevent the attack from being repeated.

Thus, while the best modern ciphers may be far more resistant to cryptanalysis than the Enigma, cryptanalysis and the broader field of information security remain quite active.

The results of cryptanalysis

The decrypted Zimmermann Telegram.

Successful cryptanalysis has undoubtedly influenced history; the ability to read the presumed-secret thoughts and plans of others can be a decisive advantage. For example, in England in 1587, Mary, Queen of Scots was tried and executed for treason for her involvement in three plots to assassinate Elizabeth I of England which were known about because her coded correspondence with fellow conspirators had been deciphered by Thomas Phelippes; in World War I, the breaking of the Zimmermann Telegram was instrumental in bringing the United States into the war; in World War II, the cryptanalysis of the German ciphers — including the Enigma machine and the Lorenz cipher — has been credited with everything between shortening the end of the European war by a few months to determining the eventual result (see Ultra). The United States also benefited from the cryptanalysis of the Japanese Purple code (see Magic).

Governments have long recognized the potential benefits of cryptanalysis for intelligence, both military and diplomatic, and established dedicated organizations devoted to breaking the codes and ciphers of other nations, for example, GCHQ and the NSA, organizations which are still very active today. In 2004, it was reported that the United States had broken Iranian ciphers. (It is unknown, however, whether this was pure cryptanalysis, or whether other factors were involved:

Types of cryptanalytic attack

Cryptanalytic attacks vary in potency and how much of a threat they pose to real-world cryptosystems. A certificational weakness is a theoretical attack that is unlikely to be applicable in any real-world situation; the majority of results found in modern cryptanalytic research are of this type. Essentially, the practical importance of an attack is dependent on the answers to the following four questions:

    What knowledge and capabilities does the attacker need?
    How much additional secret information is deduced?
    How much computation is required? (What is the computational complexity?)
    Does the attack break the full cryptosystem, or only a weakened version?

Access needed for the attack

Cryptanalysis can be performed under a number of assumptions about how much access the attacker has to the system under attack. As a basic starting point it is normally assumed that, for the purposes of analysis, the general algorithm is known; this is Kerckhoffs' principle of "the enemy knows the system". This is a reasonable assumption in practice — throughout history, there are countless examples of secret algorithms falling into wider knowledge, variously through espionage, betrayal and reverse engineering. (On occasion, ciphers have been reconstructed through pure deduction; for example, the German Lorenz cipher and the Japanese Purple code, and a variety of classical schemes).

Other assumptions include:

    Ciphertext-only: the cryptanalyst has access only to a collection of ciphertexts or codetexts.
    Known-plaintext: the attacker has a set of ciphertexts to which he knows the corresponding plaintext.
    Chosen-plaintext (chosen-ciphertext): the attacker can obtain the ciphertexts (plaintexts) corresponding to an arbitrary set of plaintexts (ciphertexts) of his own choosing.
    Adaptive chosen-plaintext: like a chosen-plaintext attack, except the attacker can choose subsequent plaintexts based on information learned from previous encryptions. Similarly Adaptive chosen ciphertext attack.
    Related-key attack: Like a chosen-plaintext attack, except the attacker can obtain ciphertexts encrypted under two different keys. The keys are unknown, but the relationship between them is known; for example, two keys that differ in the one bit.

These types of attack clearly differ in how plausible they would be to mount in practice. Although some are more likely than others, cryptographers will often take a conservative approach to security and assume the worst-case when designing algorithms, reasoning that if a scheme is secure even against unrealistic threats, then it should also resist real-world cryptanalysis as well.

The assumptions are often more realistic than they might seem upon first glance. For a known-plaintext attack, the cryptanalyst might well know or be able to guess at a likely part of the plaintext, such as an encrypted letter beginning with "Dear Sir", or a computer session starting with "LOGIN:". A chosen-plaintext attack is less likely, but it is sometimes plausible: for example, you could convince someone to forward a message you have given them, but in encrypted form. Related-key attacks are mostly theoretical, although they can be realistic in certain situations, for example, when constructing cryptographic hash functions using a block cipher.

Usefulness of attack results

The results of cryptanalysis can also vary in usefulness. For example, cryptographer Lars Knudsen (1998) classified various types of attack on block ciphers according to the amount and quality of secret information that was discovered:

    Total break — the attacker deduces the secret key.
    Global deduction — the attacker discovers a functionally equivalent algorithm for encryption and decryption, but without learning the key.
    Instance (local) deduction — the attacker discovers additional plaintexts (or ciphertexts) not previously known.
    Information deduction — the attacker gains some Shannon information about plaintexts (or ciphertexts) not previously known.
    Distinguishing algorithm — the attacker can distinguish the cipher from a random permutation.

Similar considerations apply to attacks on other types of cryptographic algorithm.
[edit] Computational resources required

Attacks can also be characterised by the resources they require. Those resources include:

    Time — the number of computation steps (like encryptions) which must be performed.
    Memory — the amount of storage required to perform the attack.
    Data — the quantity of plaintexts and ciphertexts required.

It's sometimes difficult to predict these quantities precisely, especially when the attack isn't practical to actually implement for testing. But academic cryptanalysts tend to provide at least the estimated order of magnitude of their attacks' difficulty, saying, for example, "SHA-1 collisions now 252"

Bruce Schneier notes that even computationally impractical attacks can be considered breaks: "Breaking a cipher simply means finding a weakness in the cipher that can be exploited with a complexity less than brute force. Never mind that brute-force might require 2128 encryptions; an attack requiring 2110 encryptions would be considered a break...simply put, a break can just be a certificational weakness: evidence that the cipher does not perform as advertised."

Partial breaks

Academic attacks are often against weakened versions of a cryptosystem, such as a block cipher or hash function with some rounds removed. Many, but not all, attacks become exponentially more difficult to execute as rounds are added to a cryptosystem, so it's possible for the full cryptosystem to be strong even though reduced-round variants are weak. Nonetheless, partial breaks that come close to breaking the original cryptosystem may mean that a full break will follow; the successful attacks on DES, MD5, and SHA-1 were all preceded by attacks on weakened versions.

Academic weakness versus practical weakness

In academic cryptography, a weakness or a break in a scheme is usually defined quite conservatively: it might require impractical amounts of time, memory, or known plaintexts. It also might require the attacker be able to do things many real-world attackers can't: for example, the attacker may need to choose particular plaintexts to be encrypted or even to ask for plaintexts to be encrypted using several keys related to the secret key. Furthermore, it might only reveal a small amount of information, enough to prove the cryptosystem imperfect but too little to be useful to real-world attackers. Finally, an attack might only apply to a weakened version of cryptographic tools, like a reduced-round block cipher, as a step towards breaking of the full system.

 

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