"A hash function is any function that can be used to map data of arbitrary size to fixed-size values..."
A mathematical function that takes input data and produces a fixed-size string of characters.
Cryptography Basics: Understanding the basics of cryptography is essential to understand hash functions. It includes the history, terminology, classification, and key concepts of cryptography.
Message Authentication Codes (MAC): MAC is a technique that helps to ensure that the message is not tampered with during transmission. It uses a shared secret key to generate a code, which is attached to the message.
Digital Signatures: A digital signature is a type of cryptographic method that provides authenticity and non-repudiation of the message. It uses public-key cryptography to sign the message.
Collision resistance: Collision resistance is a property of hash functions that ensures that it is practically infeasible to find two messages that result in the same hash value.
One-way functions: One-way functions are the cryptographic functions that are easy to calculate in one direction but hard to calculate in the other direction.
Merkle-Damgard construction: Merkle-Damgard construction is a method to build hash functions. It divides the message into blocks and processes them one at a time.
Birthday paradox: The birthday paradox is a probability theory that explains the likelihood of finding two people with the same birthday. It is applicable to hash functions, where it explains the likelihood of finding two messages with the same hash value.
SHA (Secure Hash Algorithm): SHA is a family of cryptographic hash functions that are widely used in various security applications. It includes SHA-1, SHA-2, and SHA-3.
Cryptanalysis of hash functions: Cryptanalysis is a technique to break the cryptographic security of hash functions. It includes various attacks like birthday attacks, brute-force attacks, and collision attacks.
Applications of hash functions: Hash functions have various applications in cryptography, including password hashing, digital signature, message authentication, and secure file transfer.
MD5 (Message Digest 5): A widely used hash function that generates a fixed-length output of 128 bits. It is no longer considered secure and has been supplanted by newer and more secure hash functions.
SHA-1 (Secure Hash Algorithm 1): A hash function used for digital signatures and other cryptographic applications. It generates a fixed-length output of 160 bits and is considered to be relatively secure, although its use is being phased out.
SHA-2 (Secure Hash Algorithm 2): A family of hash functions, including SHA-224, SHA-256, SHA-384, and SHA-512, that generate output lengths of 224, 256, 384, and 512 bits, respectively. SHA-2 is widely used and considered to be secure.
SHA-3 (Secure Hash Algorithm 3): A family of hash functions, including SHA3-224, SHA3-256, SHA3-384, and SHA3-512, that generate output lengths of 224, 256, 384, and 512 bits, respectively. SHA-3 was designed to be even more secure than SHA-2.
BLAKE (Block Length Adaptive Secure Hash Algorithm): A family of hash functions that can generate output lengths of 224, 256, 384, and 512 bits. BLAKE is notable for its speed and security.
Whirlpool: A hash function that generates a fixed-length output of 512 bits. It is designed to be secure and is used in digital forensics and other security applications.
RIPEMD (RACE Integrity Primitives Evaluation Message Digest): A family of hash functions, including RIPEMD-128, RIPEMD-160, RIPEMD-256, and RIPEMD-320, that generate output lengths of 128, 160, 256, and 320 bits, respectively. RIPEMD is used in various cryptographic applications.
Tiger: A hash function that generates a fixed-length output of 192 bits. It is designed to be fast and secure and is used in various applications, including password storage.
GOST (Gostral Otchetnij Storon Technical Committee): A family of hash functions, including GOST R 34.11-94, GOST R 34.311-2012, and GOST R 34.11-2018, that generate output lengths of 256 and 512 bits. GOST is used in various applications, including digital signatures.
Skein: A family of hash functions that generate output lengths of up to 4096 bits. Skein is designed to be a fast and secure alternative to other hash functions, and is used in various applications, including password storage and digital signatures.
Keccak: A family of hash functions, including Keccak-224, Keccak-256, Keccak-384, and Keccak-512, that generate output lengths of 224, 256, 384, and 512 bits, respectively. Keccak is the underlying algorithm of SHA-3, and is designed to be secure and versatile.
Bcrypt: A hash function designed specifically for password storage. It generates a fixed-length output of 192 bits and is designed to be slow and computationally intensive to deter brute-force attacks.
"The values returned by a hash function are called hash values, hash codes, digests, or simply hashes."
"The values are usually used to index a fixed-size table called a hash table."
"Use of a hash function to index a hash table is called hashing or scatter storage addressing."
"Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees..."
"They require an amount of storage space only fractionally greater than the total space required for the data or records themselves."
"Use of hash functions relies on statistical properties of key and function interaction: worst-case behaviour is intolerably bad but rare, and average-case behaviour can be nearly optimal (minimal collision)."
"Hash functions are related to (and often confused with) checksums, check digits, fingerprints, lossy compression, randomization functions, error-correcting codes, and ciphers."
"Although the concepts overlap to some extent, each one has its own uses and requirements and is designed and optimized differently."
"The hash function differs from these concepts mainly in terms of data integrity."
"...though there are some hash functions that support variable length output."
"The values are usually used to index a fixed-size table called a hash table."
"Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees..."
"Worst-case behaviour is intolerably bad but rare, and average-case behaviour can be nearly optimal (minimal collision)."
"Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval."
"Hashing is a computationally and storage space-efficient form of data access that avoids...the often exponential storage requirements of direct access of state spaces of large or variable-length keys."
"The often exponential storage requirements of direct access of state spaces of large or variable-length keys."
"...each one has its own uses and requirements and is designed and optimized differently."
"...each one has its own uses and requirements and is designed and optimized differently."
"...each one has its own uses and requirements and is designed and optimized differently."