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1. ### Cryptography - Wikipedia

en.wikipedia.org/wiki/Cryptography

Cryptography, or cryptology (from Ancient Greek: κρυπτός, romanized: kryptós "hidden, secret"; and γράφειν graphein, "to write", or -λογία-logia, "study", respectively), is the practice and study of techniques for secure communication in the presence of third parties called adversaries.

• Lorenz Cipher

The Lorenz SZ40, SZ42a and SZ42b were German rotor stream...

• Block Ciphers

In cryptography, a block cipher is a deterministic algorithm...

2. ### Cryptography - Simple English Wikipedia, the free encyclopedia

simple.wikipedia.org/wiki/Cryptography

Cryptography, or cryptology, is the practice and study of hiding information. It is sometimes called code, but this is not really a correct name. It is the science used to try to keep information secret and safe. Modern cryptography is a mix of mathematics, computer science, and electrical engineering.

3. ### History of cryptography - Wikipedia

en.wikipedia.org/wiki/History_of_cryptography

Cryptography, the use of codes and ciphers to protect secrets, began thousands of years ago. Until recent decades, it has been the story of what might be called classic cryptography — that is, of methods of encryption that use pen and paper, or perhaps simple mechanical aids.

4. ### Public-key cryptography - Wikipedia

en.wikipedia.org/wiki/Public-key_cryptography
• Overview
• Description
• Applications
• Weaknesses
• Examples
• History

Public-key cryptography, or asymmetric cryptography, is a cryptographic system that uses pairs of keys: public keys, which may be disseminated widely, and private keys, which are known only to the owner. The generation of such keys depends on cryptographic algorithms based on mathematical problems to produce one-way functions. Effective security only requires keeping the private key private; the public key can be openly distributed without compromising security. In such a system, any person can

Before the mid-1970s, all cipher systems used symmetric key algorithms, in which the same cryptographic key is used with the underlying algorithm by both the sender and the recipient, who must both keep it secret. Of necessity, the key in every such system had to be exchanged between the communicating parties in some secure way prior to any use of the system – a secure channel. This requirement is never trivial and very rapidly becomes unmanageable as the number of participants increases ...

The most obvious application of a public key encryption system is in encrypting communication to provide confidentiality – a message that a sender encrypts using the recipient's public key can be decrypted only by the recipient's paired private key. Another application in public key cryptography is the digital signature. Digital signature schemes can be used for sender authentication. Non-repudiation systems use digital signatures to ensure that one party cannot successfully dispute its ...

As with all security-related systems, it is important to identify potential weaknesses.

Examples of well-regarded asymmetric key techniques for varied purposes include

During the early history of cryptography, two parties would rely upon a key that they would exchange by means of a secure, but non-cryptographic, method such as a face-to-face meeting or a trusted courier. This key, which both parties kept absolutely secret, could then be used to exchange encrypted messages. A number of significant practical difficulties arise with this approach to distributing keys.

What are the types of public key cryptography?

How does public-key cryptography work?

What is the history of cryptography?

Is cryptography computer science?

6. ### Quantum cryptography - Wikipedia

en.wikipedia.org/wiki/Quantum_cryptography

Quantum cryptography is the science of exploiting quantum mechanical properties to perform cryptographic tasks. The best known example of quantum cryptography is quantum key distribution which offers an information-theoretically secure solution to the key exchange problem.

7. ### Post-quantum cryptography - Wikipedia

en.wikipedia.org/wiki/Post-quantum_cryptography
• Overview
• Algorithms
• Security reductions
• Comparison
• Forward secrecy

Post-quantum cryptography refers to cryptographic algorithms that are thought to be secure against an attack by a quantum computer. As of 2020, this is not true for the most popular public-key algorithms, which can be efficiently broken by a sufficiently strong quantum computer. The problem with currently popular algorithms is that their security relies on one of three hard mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve discrete log

Currently post-quantum cryptography research is mostly focused on six different approaches

In cryptography research, it is desirable to prove the equivalence of a cryptographic algorithm and a known hard mathematical problem. These proofs are often called "security reductions", and are used to demonstrate the difficulty of cracking the encryption algorithm. In other words, the security of a given cryptographic algorithm is reduced to the security of a known hard problem. Researchers are actively looking for security reductions in the prospects for post quantum cryptography. Current re

The fundamental idea of using LWE and Ring LWE for key exchange was proposed and filed at the University of Cincinnati in 2011 by Jintai Ding. The basic idea comes from the associativity of matrix multiplications, and the errors are used to provide the security. The paper appeare

For 128 bits of security in NTRU, Hirschhorn, Hoffstein, Howgrave-Graham and Whyte, recommend using a public key represented as a degree 613 polynomial with coefficients mod {\\displaystyle {\\bmod {\\left}}}. This results in a public key of 6130 bits. The corresponding private key

For 128 bits of security and the smallest signature size in a Rainbow multivariate quadratic equation signature scheme, Petzoldt, Bulygin and Buchmann, recommend using equations in F 31 {\\displaystyle \\mathbb {F} _{31}} with a public key size of just over 991,000 bits, a private

A public-key system demonstrates a property referred to as perfect forward secrecy when it generates random public keys per session for the purposes of key agreement. This means that the compromise of one message cannot lead to the compromise of others, and also that there is not a single secret value which can lead to the compromise of multiple messages. Security experts recommend using cryptographic algorithms that support forward secrecy over those that do not. The reason for this is that for

8. ### Elliptic-curve cryptography - Wikipedia

en.wikipedia.org/wiki/Elliptic-curve_cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields.ECC allows smaller keys compared to non-EC cryptography (based on plain Galois fields) to provide equivalent security.

9. ### Code (cryptography) - Wikipedia

en.wikipedia.org/wiki/Code_(cryptography)
• Overview
• One- and two-part codes
• One-time code
• Idiot code
• Cryptanalysis of codes
• Superencipherment

In cryptology, a code is a method used to encrypt a message that operates at the level of meaning; that is, words or phrases are converted into something else. A code might transform "change" into "CVGDK" or "cocktail lounge". The U.S. National Security Agency defined a code as "A substitution cryptosystem in which the plaintext elements are primarily words, phrases, or sentences, and the code equivalents typically consist of letters or digits in otherwise meaningless combinations of identical l

Codes are defined by "codebooks", which are dictionaries of codegroups listed with their corresponding plaintext. Codes originally had the codegroups assigned in 'plaintext order' for convenience of the code designed, or the encoder. For example, in a code using numeric code groups, a plaintext word starting with "a" would have a low-value group, while one starting with "z" would have a high-value group. The same codebook could be used to "encode" a plaintext message into a coded message or "cod

A one-time code is a prearranged word, phrase or symbol that is intended to be used only once to convey a simple message, often the signal to execute or abort some plan or confirm that it has succeeded or failed. One-time codes are often designed to be included in what would appear to be an innocent conversation. Done properly they are almost impossible to detect, though a trained analyst monitoring the communications of someone who has already aroused suspicion might be able to recognize a comm

An idiot code is a code that is created by the parties using it. This type of communication is akin to the hand signals used by armies in the field. Example: Any sentence where 'day' and 'night' are used means 'attack'. The location mentioned in the following sentence specifies the location to be attacked. Plaintext: Attack X. Codetext: We walked day and night through the streets but couldn't find it! Tomorrow we'll head into X. An early use of the term appears to be by George Perrault, a charac

While solving a monoalphabetic substitution cipher is easy, solving even a simple code is difficult. Decrypting a coded message is a little like trying to translate a document written in a foreign language, with the task basically amounting to building up a "dictionary" of the codegroups and the plaintext words they represent. One fingerhold on a simple code is the fact that some words are more common than others, such as "the" or "a" in English. In telegraphic messages, the codegroup for "STOP"

It was common to encipher a message after first encoding it, to increase the difficulty of cryptanalysis. With a numerical code, this was commonly done with an "additive" - simply a long key number which was digit-by-digit added to the code groups, modulo 10. Unlike the codebooks, additives would be changed frequently. The famous Japanese Navy code, JN-25, was of this design.

10. ### Key (cryptography) - Wikipedia

en.wikipedia.org/wiki/Key_(cryptography)
• Overview
• Need for secrecy
• Key scope
• Ownership and revocation
• Key sizes
• Key choice

In cryptography, a key is a piece of information that determines the functional output of a cryptographic algorithm. For encryption algorithms, a key specifies the transformation of plaintext into ciphertext, and vice versa for decryption algorithms. Keys also specify transformations in other cryptographic algorithms, such as digital signature schemes and message authentication codes.

In designing security systems, it is wise to assume that the details of the cryptographic algorithm are already available to the attacker. This is known as Kerckhoffs' principle — "only secrecy of the key provides security", or, reformulated as Shannon's maxim, "the enemy knows the system". The history of cryptography provides evidence that it can be difficult to keep the details of a widely used algorithm secret. A key is often easier to protect than an encryption algorithm, and easier ...

Keys are generated to be used with a given suite of algorithms, called a cryptosystem. Encryption algorithms which use the same key for both encryption and decryption are known as symmetric key algorithms. A newer class of "public key" cryptographic algorithms was invented in the 1970s. These asymmetric key algorithms use a pair of keys—or keypair—a public key and a private one. Public keys are used for encryption or signature verification; private ones decrypt and sign. The design is ...

Part of the security brought about by cryptography concerns confidence about who signed a given document, or who replies at the other side of a connection. Assuming that keys are not compromised, that question consists of determining the owner of the relevant public key. To be able to tell a key's owner, public keys are often enriched with attributes such as names, addresses, and similar identifiers. The packed collection of a public key and its attributes can be digitally signed by one or more

For the one-time pad system the key must be at least as long as the message. In encryption systems that use a cipher algorithm, messages can be much longer than the key. The key must, however, be long enough so that an attacker cannot try all possible combinations. A key length of 80 bits is generally considered the minimum for strong security with symmetric encryption algorithms. 128-bit keys are commonly used and considered very strong. See the key size article for a more complete discussion.

To prevent a key from being guessed, keys need to be generated truly randomly and contain sufficient entropy. The problem of how to safely generate truly random keys is difficult, and has been addressed in many ways by various cryptographic systems. There is an RFC on generating randomness. Some operating systems include tools for "collecting" entropy from the timing of unpredictable operations such as disk drive head movements. For the production of small amounts of keying material, ordinary di

11. ### RSA (cryptosystem) - Wikipedia

en.wikipedia.org/wiki/RSA_(cryptosystem)

RSA (Rivest–Shamir–Adleman) is a public-key cryptosystem that is widely used for secure data transmission. It is also one of the oldest. The acronym RSA comes from the surnames of Ron Rivest, Adi Shamir, and Leonard Adleman, who publicly described the algorithm in 1977.

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