Cipher

Jai Ganesh · 2023-04-11 20:33:42

Cipher

Gist

Ciphers, also called encryption algorithms, are systems for encrypting and decrypting data. A cipher converts the original message, called plaintext, into ciphertext using a key to determine how it is done.

Ciphers are generally categorized according to how they work and by how their key is used for encryption and decryption. Block ciphers accumulate symbols in a message of a fixed size (the block), and stream ciphers work on a continuous stream of symbols. When a cipher uses the same key for encryption and decryption, they are known as symmetric key algorithms or ciphers. Asymmetric key algorithms or ciphers use a different key for encryption/decryption.

Ciphers can be complex algorithms or simple ones. A common cipher, ROT13 (or ROT-13), is a basic letter substitution cipher, shorthand for “rotate by 13 places” in the alphabet. In a message, ROT13 replaces each letter of the alphabet with the letter that is thirteen places ahead of it.

Example:

"The government of ancient Rome was among the first civilizations to use ciphers to transmit sensitive information such as military conversations."

Details

In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. To encipher or encode is to convert information into cipher or code. In common parlance, "cipher" is synonymous with "code", as they are both a set of steps that encrypt a message; however, the concepts are distinct in cryptography, especially classical cryptography.

Codes generally substitute different length strings of characters in the output, while ciphers generally substitute the same number of characters as are input. A code maps one meaning with another. Words and phrases can be coded as letters or numbers. Codes typically have direct meaning from input to key. Codes primarily function to save time. Ciphers are algorithmic. The given input must follow the cipher's process to be solved. Ciphers are commonly used to encrypt written information.

Codes operated by substituting according to a large codebook which linked a random string of characters or numbers to a word or phrase. For example, "UQJHSE" could be the code for "Proceed to the following coordinates." When using a cipher the original information is known as plaintext, and the encrypted form as ciphertext. The ciphertext message contains all the information of the plaintext message, but is not in a format readable by a human or computer without the proper mechanism to decrypt it.

The operation of a cipher usually depends on a piece of auxiliary information, called a key (or, in traditional NSA parlance, a cryptovariable). The encrypting procedure is varied depending on the key, which changes the detailed operation of the algorithm. A key must be selected before using a cipher to encrypt a message. Without knowledge of the key, it should be extremely difficult, if not impossible, to decrypt the resulting ciphertext into readable plaintext.

Most modern ciphers can be categorized in several ways

* By whether they work on blocks of symbols usually of a fixed size (block ciphers), or on a continuous stream of symbols (stream ciphers).
* By whether the same key is used for both encryption and decryption (symmetric key algorithms), or if a different key is used for each (asymmetric key algorithms). If the algorithm is symmetric, the key must be known to the recipient and sender and to no one else. If the algorithm is an asymmetric one, the enciphering key is different from, but closely related to, the deciphering key. If one key cannot be deduced from the other, the asymmetric key algorithm has the public/private key property and one of the keys may be made public without loss of confidentiality.

Etymology

Originating from the Arabic word for zero (sifr), the word “cipher” spread to Europe as part of the Arabic numeral system during the Middle Ages. The Roman numeral system lacked the concept of zero, and this limited advances in mathematics. In this transition, the word was adopted into Medieval Latin as cifra, and then into Middle French as cifre. This eventually led to the English word cipher (minority spelling cypher). One theory for how the term came to refer to encoding is that the concept of zero was confusing to Europeans, and so the term came to refer to a message or communication that was not easily understood.

The term cipher was later also used to refer to any Arabic digit, or to calculation using them, so encoding text in the form of Arabic numerals is literally converting the text to "ciphers".

Versus codes

In casual contexts, “code” and “cipher” can typically be used interchangeably, however, the technical usages of the words refer to different concepts. Codes contain meaning; words and phrases are assigned to numbers or symbols, creating a shorter message.

An example of this is the commercial telegraph code which was used to shorten long telegraph messages which resulted from entering into commercial contracts using exchanges of telegrams.

Another example is given by whole word ciphers, which allow the user to replace an entire word with a symbol or character, much like the way Japanese utilize Kanji (meaning Chinese characters in Japanese) characters to supplement their language. ex "The quick brown fox jumps over the lazy dog" becomes "The quick brown 狐 jumps 上 the lazy 犬".

Ciphers, on the other hand, work at a lower level: the level of individual letters, small groups of letters, or, in modern schemes, individual bits and blocks of bits. Some systems used both codes and ciphers in one system, using superencipherment to increase the security. In some cases the terms codes and ciphers are also used synonymously to substitution and transposition.

Historically, cryptography was split into a dichotomy of codes and ciphers; and coding had its own terminology, analogous to that for ciphers: "encoding, codetext, decoding" and so on.

However, codes have a variety of drawbacks, including susceptibility to cryptanalysis and the difficulty of managing a cumbersome codebook. Because of this, codes have fallen into disuse in modern cryptography, and ciphers are the dominant technique.

Types

There are a variety of different types of encryption. Algorithms used earlier in the history of cryptography are substantially different from modern methods, and modern ciphers can be classified according to how they operate and whether they use one or two keys.

Historical

The Caesar Cipher is one of the earliest known cryptographic systems. Julius Caesar used a cipher that shifts the letters in the alphabet in place by three and wrapping the remaining letters to the front to write to Marcus Ciero in approximately 50 BC.

Historical pen and paper ciphers used in the past are sometimes known as classical ciphers. They include simple substitution ciphers (such as ROT13) and transposition ciphers (such as a Rail Fence Cipher). For example, "GOOD DOG" can be encrypted as "PLLX XLP" where "L" substitutes for "O", "P" for "G", and "X" for "D" in the message. Transposition of the letters "GOOD DOG" can result in "DGOGDOO". These simple ciphers and examples are easy to crack, even without plaintext-ciphertext pairs.

William Shakespeare often used the concept of ciphers in his writing to symbolize nothingness. In Shakespeare’s Henry V, he relates one of the accounting methods that brought the Arabic Numeral system and zero to Europe, to the human imagination. The actors who perform this play were not at the battles of Henry V’s reign, so they represent absence. In another sense, ciphers are important to people who work with numbers, but they do not hold value. Shakespeare used this concept to outline how those who counted and identified the dead from the battles used that information as a political weapon, furthering class biases and xenophobia.

Simple ciphers were replaced by polyalphabetic substitution ciphers (such as the Vigenère) which changed the substitution alphabet for every letter. For example, "GOOD DOG" can be encrypted as "PLSX TWF" where "L", "S", and "W" substitute for "O". With even a small amount of known or estimated plaintext, simple polyalphabetic substitution ciphers and letter transposition ciphers designed for pen and paper encryption are easy to crack. It is possible to create a secure pen and paper cipher based on a one-time pad though, but the usual disadvantages of one-time pads apply.

During the early twentieth century, electro-mechanical machines were invented to do encryption and decryption using transposition, polyalphabetic substitution, and a kind of "additive" substitution. In rotor machines, several rotor disks provided polyalphabetic substitution, while plug boards provided another substitution. Keys were easily changed by changing the rotor disks and the plugboard wires. Although these encryption methods were more complex than previous schemes and required machines to encrypt and decrypt, other machines such as the British Bombe were invented to crack these encryption methods.

Modern

Modern encryption methods can be divided by two criteria: by type of key used, and by type of input data.

By type of key used ciphers are divided into:

* symmetric key algorithms (Private-key cryptography), where one same key is used for encryption and decryption, and
AES
* asymmetric key algorithms (Public-key cryptography), where two different keys are used for encryption and decryption.

In a symmetric key algorithm (e.g., DES and AES), the sender and receiver must have a shared key set up in advance and kept secret from all other parties; the sender uses this key for encryption, and the receiver uses the same key for decryption. The design of AES (Advanced Encryption System) was beneficial because it aimed to overcome the flaws in the design of the DES (Data encryption standard). AES’s designer’s claim that the common means of modern cipher cryptanalytic attacks are ineffective against AES due to its design structure.

Ciphers can be distinguished into two types by the type of input data:

* block ciphers, which encrypt block of data of fixed size, and
* stream ciphers, which encrypt continuous streams of data.

Key size and vulnerability

In a pure mathematical attack, (i.e., lacking any other information to help break a cipher) two factors above all count:

* Computational power available, i.e., the computing power which can be brought to bear on the problem. It is important to note that average performance/capacity of a single computer is not the only factor to consider. An adversary can use multiple computers at once, for instance, to increase the speed of exhaustive search for a key (i.e., "brute force" attack) substantially.

* Key size, i.e., the size of key used to encrypt a message. As the key size increases, so does the complexity of exhaustive search to the point where it becomes impractical to crack encryption directly.
Since the desired effect is computational difficulty, in theory one would choose an algorithm and desired difficulty level, thus decide the key length accordingly.

An example of this process can be found at Key Length which uses multiple reports to suggest that a symmetrical cipher with 128 bits, an asymmetric cipher with 3072 bit keys, and an elliptic curve cipher with 256 bits, all have similar difficulty at present.

Claude Shannon proved, using information theory considerations, that any theoretically unbreakable cipher must have keys which are at least as long as the plaintext, and used only once: one-time pad.

What is a cipher?

In cryptology, the discipline concerned with the study of cryptographic algorithms, a cipher is an algorithm for encrypting and decrypting data.

Symmetric key encryption, also called secret key encryption, depends on the use of ciphers, which operate symmetrically. With symmetric encryption algorithms, the same encryption key is applied to data in the same way, whether the objective is to convert plaintext to ciphertext or ciphertext to plaintext. A cipher transforms data by processing the original, plaintext characters or other data into ciphertext. The ciphertext should appear as random data.

Traditionally, ciphers used these two main types of transformation:

* Transposition ciphers keep all the original bits of data in a byte but mix their order.
* Substitution ciphers replace specific data sequences with other data sequences. For example, one type of substitution would be to transform all bits with a value of 1 to a value of 0, and vice versa.

The data output from either method is called the ciphertext.

Modern ciphers enable private communication in many different networking protocols, including the Transport Layer Security (TLS) protocol and others that offer encryption of network traffic. Many communication technologies, including phones, digital television and ATMs, rely on ciphers to maintain security and privacy.

How do ciphers work?

A cipher uses a system of fixed rules -- an encryption algorithm -- to transform plaintext, a legible message, into ciphertext, an apparently random string of characters. Ciphers can be designed to encrypt or decrypt bits in a stream, known as stream ciphers. Or they can process ciphertext in uniform blocks of a specified number of bits, known as block ciphers.

Modern cipher implementations depend on the algorithm and a secret key, which is used by the encryption algorithm to modify data as it is encrypted. Ciphers that use longer keys, measured in bits, are more effective against brute-force attacks. The longer the key length, the more brute-force attempts are necessary to expose the plaintext. While cipher strength is not always dependent on the length of the key, experts recommend modern ciphers be configured to use keys of at least 128 bits or more, depending on the algorithm and the use case.

A key is an essential part of an encryption algorithm -- so much so that, in real-world ciphering, the key is kept secret, not the algorithm. Strong encryption algorithms are designed so that, even if someone knows the algorithm, it should be impossible to decipher ciphertext without knowing the appropriate key. Consequently, before a cipher can work, both the sender and receiver must have a key or a set of keys.

Ciphers turn plaintext into ciphertext

Cryptographic ciphers are used to convert ciphertext to plaintext and back.

With symmetric key algorithms, the same key is used for the encryption and decryption of data. Asymmetric key algorithms use public keys and private keys to encrypt and decrypt data.

In asymmetric cryptography, also known as public key cryptography, the keys are large numbers that have been paired together but are not identical (asymmetric). Key pairs include the following:

* The public key can be shared with everyone.
* The private, or secret key, is kept secret.

Either of the keys can be used to encrypt a message; the opposite key from the one used to encrypt the message is used for decryption.

The private or secret key of the pair is used by the owner of the key pair to decrypt or encrypt data, while the public key is used by anyone who wants to encrypt a message that can be decrypted only by the holder of the private key.

Symmetric encryption algorithms use just one key for both encryption and decryption, while asymmetric encryption algorithms use public/private key pairs.

What are ciphers used for?

Symmetric ciphers are most commonly used to secure online communications. They are also incorporated into many different network protocols to be used for exchanges of data. For example, Secure Sockets Layer and TLS use ciphers to encrypt application layer data, especially when used with HTTP Secure (HTTPS).

Virtual private networks that connect remote workers or remote branches to corporate networks use protocols with symmetric key algorithms to protect data communications. Symmetric ciphers protect data privacy in most Wi-Fi networks, online banking and e-commerce services, and mobile telephony.

Some protocols use asymmetric cryptography to encrypt and authenticate endpoints. They also use it to secure the exchange of symmetric keys to encrypt session data. Those protocols include the following:

* TLS
* HTTPS
* Secure Shell
* Open Pretty Good Privacy
* Secure/Multipurpose Internet Mail Extensions

While public key cryptography is considered more secure than symmetric encryption, it is also more computationally intensive. For performance reasons, protocols often rely on symmetric key algorithms to encrypt session data.

Difference between codes and ciphers

Codes and ciphers are different ways to encrypt a message. A code is a method of changing a message by replacing each word with another word that has a different meaning.

On the other hand, a cipher converts the message using its algorithm to transform the data representing the letters and words in the message. Ciphers are easier to implement and use with computers because algorithms are automated and easily programmed.

Types of ciphers

Ciphers can be characterized in different ways, including the following:

* Block ciphers encrypt uniformly sized blocks of data.
* Stream ciphers can be applied to streams of data that are often received and sent over a network.

Ciphers can depend on traditional keys used directly to key ciphertext or on elliptical curve cryptography (ECC). When ECC is used with a 160-bit key, it can provide the security of a traditional cipher, like that used in the RSA (Rivest-Shamir-Adleman) cryptosystem using a key of 1,024 bits in length.

Modern-day encryption algorithms are designed to withstand attacks even when the attacker knows what cipher is being used. Historically, ciphers have been less secure against attack because they were used to encipher plaintext by hand and could be more easily analyzed and broken with computer power.

Examples of ciphers

Some well-known historical ciphers include the following:

* Caesar. This cipher is attributed to Julius Caesar, who is said to have used it to communicate securely with his generals. It is a simple substitution cipher where each letter in the plaintext is shifted a specific number of places down the alphabet. The shift number said to be used by Caesar was three. Substitution ciphers are often implemented by writing down the plaintext alphabet, with the ciphertext alphabet written above the plaintext letters, shifted by the number those communicating agree to. A shift of three puts the letter D above the plaintext A, E above B and so on. The number of characters shifted is considered a simple form of a key.

* Atbash. This cipher is a substitution cipher in which the plaintext alphabet is mapped onto itself but in reverse order. In other words, the plaintext letter A is mapped to ciphertext Z, B is mapped to Y, C to X and so on. Atbash is named after the two first and two last letters in the Hebrew alphabet. It is thought to have been in use for hundreds of years.

* Simple substitution. This one has also been used for hundreds of years. It substitutes every plaintext character for a different ciphertext character, resulting in what is effectively a 26-character key. It differs from the Caesar cipher because the enciphering alphabet is completely jumbled, rather than simply shifted a uniform number of places.

* Vigenère. This cipher is a form of polyalphabetic substitution, meaning it is based on substitution using multiple substitution alphabets. The Vigenère cipher uses a series of interwoven Caesar ciphers, based on the letters of a keyword. The original text is encrypted using what is known as the Vigenère square or Vigenère table.

* Homophonic substitution. This substitution cipher uses several different ciphertext letters to replace single plaintext letters. This type of cipher is typically much more difficult to break than standard substitution ciphers.

These historical ciphers are still relevant because they use different fundamental components of modern ciphers, such as substitution and transposition.

Ciphers can go in and out of fashion, depending on their track records for strength against attacks, as well as the discovery of new attack vectors. Learn about the first steps to using ciphers securely by understanding the basics of symmetric key encryption algorithms.

Math Is Fun Forum

#1 2023-04-11 20:33:42

Cipher

Board footer