Cryptography

Home > Mathematics > Cryptography

The study of encoding and decoding secret messages based on mathematical algorithms.

Encryption: The process of encoding data in such a way that only authorized parties can read it.

Decryption: The process of converting encrypted data back into its original, readable form.

Key: A code or number that is used to encrypt and decrypt data.

Symmetric Cryptography: A type of cryptography that uses the same key for encryption and decryption.

Asymmetric Cryptography: A type of cryptography that uses a public key for encryption and a private key for decryption.

Hash Function: A mathematical function that takes input data and produces a fixed-size string of characters.

Digital Signature: A mathematical technique used to validate the authenticity and integrity of a message.

Certificate Authority (CA): An entity that issues digital certificates for use in electronic transactions.

Public Key Infrastructure (PKI): A system for managing the creation, distribution, and revocation of digital certificates.

Cryptanalysis: The study of cryptographic techniques with the intention of weakening or breaking them.

One-Time Pad: A type of encryption that uses a random key that is as long as the plaintext.

Block Cipher: A type of encryption that encrypts data one block at a time.

Stream Cipher: A type of encryption that encrypts data one bit or byte at a time.

Side-Channel Attacks: Attacks that exploit weaknesses in a system's physical implementation, rather than in its cryptographic algorithms.

Quantum Cryptography: A type of encryption that uses the properties of quantum mechanics to secure communications.

What is cryptography?

- "Cryptography, or cryptology, is the practice and study of techniques for secure communication in the presence of adversarial behavior."

Which subjects does modern cryptography intersect with?

- "Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others."

What are the core concepts related to information security?

- "Core concepts related to information security (data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography."

Can you provide some practical applications of cryptography?

- "Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications."

What was the primary purpose of cryptography in the past?

- "Cryptography prior to the modern age was effectively synonymous with encryption, converting readable information (plaintext) to unintelligible nonsense text (ciphertext), which can only be read by reversing the process (decryption)."

How do senders ensure only intended recipients can access encrypted messages?

- "The sender of an encrypted (coded) message shares the decryption (decoding) technique only with the intended recipients to preclude access from adversaries."

Who are the commonly used names in cryptography literature for sender, recipient, and eavesdropping adversary?

- "The cryptography literature often uses the names 'Alice' (or 'A') for the sender, 'Bob' (or 'B') for the intended recipient, and 'Eve' (or 'E') for the eavesdropping adversary."

What has led to the increased complexity and variety of cryptography methods?

- "Since the development of rotor cipher machines in World War I and the advent of computers in World War II, cryptography methods have become increasingly complex and their applications more varied."

What is the basis of modern cryptography?

- "Modern cryptography is heavily based on mathematical theory and computer science practice; cryptographic algorithms are designed around computational hardness assumptions."

How are well-designed cryptographic schemes described?

- "Such schemes, if well designed, are therefore termed 'computationally secure'."

What factors require continual reevaluation and adaptation of cryptographic designs?

- "Theoretical advances (e.g., improvements in integer factorization algorithms) and faster computing technology require these designs to be continually reevaluated and, if necessary, adapted."

Is it theoretically possible to break into a well-designed system?

- "While it is theoretically possible to break into a well-designed system, it is infeasible in actual practice to do so."

What is the term for schemes that cannot be broken even with unlimited computing power?

- "Information-theoretically secure schemes that provably cannot be broken even with unlimited computing power, such as the one-time pad, are much more difficult to use in practice than the best theoretically breakable but computationally secure schemes."

What legal issues has the growth of cryptographic technology raised?

- "The growth of cryptographic technology has raised a number of legal issues in the Information Age."

How do governments classify cryptography?

- "Cryptography's potential for use as a tool for espionage and sedition has led many governments to classify it as a weapon and to limit or even prohibit its use and export."

Are investigators allowed to compel the disclosure of encryption keys in some jurisdictions?

- "In some jurisdictions where the use of cryptography is legal, laws permit investigators to compel the disclosure of encryption keys for documents relevant to an investigation."

What role does cryptography play in digital rights management and copyright disputes?

- "Cryptography also plays a major role in digital rights management and copyright infringement disputes with regard to digital media."