This fundamental principle was first explicitly stated in by Auguste Kerckhoffs and is generally called Kerckhoffs's Principle ; alternatively and more bluntly, it was restated by Claude Shannon , the inventor of information theory and the fundamentals of theoretical cryptography, as Shannon's Maxim —'the enemy knows the system'. Different physical devices and aids have been used to assist with ciphers.
One of the earliest may have been the scytale of ancient Greece , a rod supposedly used by the Spartans as an aid for a transposition cipher. In medieval times, other aids were invented such as the cipher grille , which was also used for a kind of steganography. With the invention of polyalphabetic ciphers came more sophisticated aids such as Alberti's own cipher disk , Johannes Trithemius ' tabula recta scheme, and Thomas Jefferson 's wheel cypher not publicly known, and reinvented independently by Bazeries around Prior to the early 20th century, cryptography was mainly concerned with linguistic and lexicographic patterns.
Since then the emphasis has shifted, and cryptography now makes extensive use of mathematics, including aspects of information theory , computational complexity , statistics , combinatorics , abstract algebra , number theory , and finite mathematics generally. Cryptography is also a branch of engineering , but an unusual one since it deals with active, intelligent, and malevolent opposition; other kinds of engineering e. There is also active research examining the relationship between cryptographic problems and quantum physics.
Just as the development of digital computers and electronics helped in cryptanalysis, it made possible much more complex ciphers. Furthermore, computers allowed for the encryption of any kind of data representable in any binary format, unlike classical ciphers which only encrypted written language texts; this was new and significant. Computer use has thus supplanted linguistic cryptography, both for cipher design and cryptanalysis. Many computer ciphers can be characterized by their operation on binary bit sequences sometimes in groups or blocks , unlike classical and mechanical schemes, which generally manipulate traditional characters i.
However, computers have also assisted cryptanalysis, which has compensated to some extent for increased cipher complexity.
Nonetheless, good modern ciphers have stayed ahead of cryptanalysis; it is typically the case that use of a quality cipher is very efficient i. Cryptanalysis of the new mechanical devices proved to be both difficult and laborious. In the United Kingdom, cryptanalytic efforts at Bletchley Park during WWII spurred the development of more efficient means for carrying out repetitious tasks. Extensive open academic research into cryptography is relatively recent; it began only in the mids. In recent times, IBM personnel designed the algorithm that became the Federal i.
Since then, cryptography has become a widely used tool in communications, computer networks , and computer security generally. Some modern cryptographic techniques can only keep their keys secret if certain mathematical problems are intractable , such as the integer factorization or the discrete logarithm problems, so there are deep connections with abstract mathematics.
There are very few cryptosystems that are proven to be unconditionally secure. The one-time pad is one, and was proven to be so by Claude Shannon. There are a few important algorithms that have been proven secure under certain assumptions. For example, the infeasibility of factoring extremely large integers is the basis for believing that RSA is secure, and some other systems, but even so proof of unbreakability is unavailable since the underlying mathematical problem remains open. In practice, these are widely used, and are believed unbreakable in practice by most competent observers.
The discrete logarithm problem is the basis for believing some other cryptosystems are secure, and again, there are related, less practical systems that are provably secure relative to the solvability or insolvability discrete log problem. As well as being aware of cryptographic history, cryptographic algorithm and system designers must also sensibly consider probable future developments while working on their designs.
For instance, continuous improvements in computer processing power have increased the scope of brute-force attacks , so when specifying key lengths , the required key lengths are similarly advancing. Symmetric-key cryptography refers to encryption methods in which both the sender and receiver share the same key or, less commonly, in which their keys are different, but related in an easily computable way. This was the only kind of encryption publicly known until June Symmetric key ciphers are implemented as either block ciphers or stream ciphers.
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A block cipher enciphers input in blocks of plaintext as opposed to individual characters, the input form used by a stream cipher. Many, even some designed by capable practitioners, have been thoroughly broken, such as FEAL. Stream ciphers, in contrast to the 'block' type, create an arbitrarily long stream of key material, which is combined with the plaintext bit-by-bit or character-by-character, somewhat like the one-time pad.
In a stream cipher, the output stream is created based on a hidden internal state that changes as the cipher operates. That internal state is initially set up using the secret key material. RC4 is a widely used stream cipher. Cryptographic hash functions are a third type of cryptographic algorithm. They take a message of any length as input, and output a short, fixed length hash , which can be used in for example a digital signature.
For good hash functions, an attacker cannot find two messages that produce the same hash. MD4 is a long-used hash function that is now broken; MD5 , a strengthened variant of MD4, is also widely used but broken in practice.
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The US National Security Agency developed the Secure Hash Algorithm series of MD5-like hash functions: SHA-0 was a flawed algorithm that the agency withdrew; SHA-1 is widely deployed and more secure than MD5, but cryptanalysts have identified attacks against it; the SHA-2 family improves on SHA-1, but is vulnerable to clashes as of ; and the US standards authority thought it "prudent" from a security perspective to develop a new standard to "significantly improve the robustness of NIST 's overall hash algorithm toolkit.
Cryptographic hash functions are used to verify the authenticity of data retrieved from an untrusted source or to add a layer of security. Message authentication codes MACs are much like cryptographic hash functions, except that a secret key can be used to authenticate the hash value upon receipt; [4] this additional complication blocks an attack scheme against bare digest algorithms , and so has been thought worth the effort.
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Symmetric-key cryptosystems use the same key for encryption and decryption of a message, although a message or group of messages can have a different key than others. A significant disadvantage of symmetric ciphers is the key management necessary to use them securely.
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Each distinct pair of communicating parties must, ideally, share a different key, and perhaps for each ciphertext exchanged as well. The number of keys required increases as the square of the number of network members, which very quickly requires complex key management schemes to keep them all consistent and secret. In a groundbreaking paper, Whitfield Diffie and Martin Hellman proposed the notion of public-key also, more generally, called asymmetric key cryptography in which two different but mathematically related keys are used—a public key and a private key. Instead, both keys are generated secretly, as an interrelated pair.
In public-key cryptosystems, the public key may be freely distributed, while its paired private key must remain secret. In a public-key encryption system, the public key is used for encryption, while the private or secret key is used for decryption. While Diffie and Hellman could not find such a system, they showed that public-key cryptography was indeed possible by presenting the Diffie—Hellman key exchange protocol, a solution that is now widely used in secure communications to allow two parties to secretly agree on a shared encryption key. Diffie and Hellman's publication sparked widespread academic efforts in finding a practical public-key encryption system.
The Diffie—Hellman and RSA algorithms, in addition to being the first publicly known examples of high quality public-key algorithms, have been among the most widely used. Other asymmetric-key algorithms include the Cramer—Shoup cryptosystem , ElGamal encryption , and various elliptic curve techniques. Ellis had conceived the principles of asymmetric key cryptography. Williamson is claimed to have developed the Diffie—Hellman key exchange. Public-key cryptography is also used for implementing digital signature schemes. A digital signature is reminiscent of an ordinary signature ; they both have the characteristic of being easy for a user to produce, but difficult for anyone else to forge.
Digital signatures can also be permanently tied to the content of the message being signed; they cannot then be 'moved' from one document to another, for any attempt will be detectable. In digital signature schemes, there are two algorithms: one for signing , in which a secret key is used to process the message or a hash of the message, or both , and one for verification , in which the matching public key is used with the message to check the validity of the signature. Digital signatures are central to the operation of public key infrastructures and many network security schemes e.
Public-key algorithms are most often based on the computational complexity of "hard" problems, often from number theory. For example, the hardness of RSA is related to the integer factorization problem, while Diffie—Hellman and DSA are related to the discrete logarithm problem. The security of elliptic curve cryptography is based on number theoretic problems involving elliptic curves.
Because of the difficulty of the underlying problems, most public-key algorithms involve operations such as modular multiplication and exponentiation, which are much more computationally expensive than the techniques used in most block ciphers, especially with typical key sizes. As a result, public-key cryptosystems are commonly hybrid cryptosystems , in which a fast high-quality symmetric-key encryption algorithm is used for the message itself, while the relevant symmetric key is sent with the message, but encrypted using a public-key algorithm.
Similarly, hybrid signature schemes are often used, in which a cryptographic hash function is computed, and only the resulting hash is digitally signed. The goal of cryptanalysis is to find some weakness or insecurity in a cryptographic scheme, thus permitting its subversion or evasion. It is a common misconception that every encryption method can be broken.
In connection with his WWII work at Bell Labs , Claude Shannon proved that the one-time pad cipher is unbreakable, provided the key material is truly random , never reused, kept secret from all possible attackers, and of equal or greater length than the message.
In such cases, effective security could be achieved if it is proven that the effort required i. This means it must be shown that no efficient method as opposed to the time-consuming brute force method can be found to break the cipher. Since no such proof has been found to date, the one-time-pad remains the only theoretically unbreakable cipher. Although well-implemented one-time-pad encryption cannot be broken, traffic analysis is still possible. There are a wide variety of cryptanalytic attacks, and they can be classified in any of several ways.
A common distinction turns on what Eve an attacker knows and what capabilities are available. In a ciphertext-only attack , Eve has access only to the ciphertext good modern cryptosystems are usually effectively immune to ciphertext-only attacks. In a known-plaintext attack , Eve has access to a ciphertext and its corresponding plaintext or to many such pairs. In a chosen-plaintext attack , Eve may choose a plaintext and learn its corresponding ciphertext perhaps many times ; an example is gardening , used by the British during WWII.
In a chosen-ciphertext attack , Eve may be able to choose ciphertexts and learn their corresponding plaintexts. Cryptanalysis of symmetric-key ciphers typically involves looking for attacks against the block ciphers or stream ciphers that are more efficient than any attack that could be against a perfect cipher.
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For example, a simple brute force attack against DES requires one known plaintext and 2 55 decryptions, trying approximately half of the possible keys, to reach a point at which chances are better than even that the key sought will have been found. But this may not be enough assurance; a linear cryptanalysis attack against DES requires 2 43 known plaintexts with their corresponding ciphertexts and approximately 2 43 DES operations. Public-key algorithms are based on the computational difficulty of various problems. The most famous of these are the difficulty of integer factorization of semiprimes and the difficulty of calculating discrete logarithms , both of which are not yet proven to be solvable in polynomial time using only a classical Turing-complete computer.
Much public-key cryptanalysis concerns designing algorithms in P that can solve these problems, or using other technologies, such as quantum computers. For instance, the best known algorithms for solving the elliptic curve-based version of discrete logarithm are much more time-consuming than the best known algorithms for factoring, at least for problems of more or less equivalent size. Thus, other things being equal, to achieve an equivalent strength of attack resistance, factoring-based encryption techniques must use larger keys than elliptic curve techniques.
For this reason, public-key cryptosystems based on elliptic curves have become popular since their invention in the mids. While pure cryptanalysis uses weaknesses in the algorithms themselves, other attacks on cryptosystems are based on actual use of the algorithms in real devices, and are called side-channel attacks.