As society becomes increasingly digital and interconnected, protecting users’ security and privacy online has never been more important. With billions of people sharing vast amounts of sensitive data every day, from financial information to personal messages, it is critical that this data remains safe from would-be hackers and other cyber threats. This is where cryptographic hash functions play a pivotal role.
Cryptographic hash functions are mathematical algorithms that take a piece of digital information, such as a text file, and convert it into a seemingly random string of characters known as a hash value or hash digest. Modern cryptography relies heavily on these functions to ensure the confidentiality, integrity and authenticity of digital communications and stored information.
Cryptographic hashes essentially act as digital fingerprints. By comparing the hashes of files or messages, one can detect even slight changes to the underlying data. This makes hashes ideal for verifying data integrity when transmitting or storing information. Hashes are also commonly used to secure login credentials and passwords so that sensitive data is never exposed in raw text format.
As we explore the inner workings of these algorithms, their various uses and best practices, hopefully the crucial role they play in keeping our information safe will become clearer.
Key Takeaway
- Hash functions are used to secure data by generating a unique cryptographic signature for any input data. This signature, called a hash value, can be used to verify the integrity and authenticity of the original data.
- Well-known hash functions include MD5, SHA-1, SHA-256, and SHA-512. They take a message of any size and output a fixed-size string, typically 128-512 bits. The same input always produces the same hash.
- Hash functions are one-way functions, meaning it is extremely difficult to derive the original input data from its hash value. However, it is easy to verify that two inputs produce the same hash value.
- Hashes are used for data integrity checks by storing the hash of a file alongside the file. The hash can later be recalculated and compared to the original to check if the file has been altered.
- Passwords are secured using hash functions to store password hashes instead of plaintext passwords. This prevents access to passwords even if the password database is compromised.
Cryptographic Hash Functions
A cryptographic hash function is distinguished from a regular hash function by additional security properties. While regular hashes focus on input size and speed of operation, cryptographic hashes are designed to withstand attacks from both outside intruders and insiders with partial information.
Some key attributes of cryptographic hash functions include:
- Collision resistance: It should be extremely difficult to find two inputs that hash to the same output.
- Pre-image resistance: Given an output, it is infeasible to find the original input.
- Second pre-image resistance: It’s computationally infeasible to find another input with the same hash as a given input.
- Avalanche effect: A small change in input completely alters the output hash in a less predictable manner.
These protections help block hash reversal, collisions and other attacks that could compromise the integrity of hashed information like passwords, signatures and document verification.
Overview of their Applications in Cryptography
Cryptographic hash functions have widespread applications across digital security domains:
- Blockchain technology relies on hashes to validate transactions and maintain integrity in distributed ledgers like Bitcoin.
- Digital signatures use hashes along with private keys to authenticate message sender identity and content.
- File integrity checking involves hashing files pre-transmission for validation after receipt.
- Passwords are securely hashed on servers using algorithms like bcrypt or scrypt for storage instead of plaintext.
- Certificate signing uses hashes and asymmetric cryptography to prove certificate authenticity and integrity.
- Watermarking and tamper detection insert and verify hashes within images, videos, code and documentation.
What is Cryptography?
Cryptography is the practice and study of techniques for securing communication and information using mathematics to encrypt and decrypt data. The main goals of cryptography are confidentiality, integrity, non-repudiation, authentication, and access control.
At a basic level, it allows two individuals, known as Helen and Job, to communicate securely over an insecure channel without their private conversation being easily intercepted or understood by an eavesdropper. Modern cryptographic systems use a variety of tools like digital signatures and certificates to provide verified transactions and online identities as well.
Conversion of Plain Message or Data into an Unrecognized Form
Fundamentally, cryptography relies on encrypting plain or intelligible information known as plaintext into an obscured form called ciphertext using an algorithm and key. Only those with the proper key can decrypt the message back into a readable format. The encryption process scrambles the message so that others cannot understand its meaning even if they intercept it.
Some examples of encryption algorithms include the Advanced Encryption Standard (AES) favored for its speed and security, the Rivest Cipher 4 (RC4) still seen in older protocols, and the RSA algorithm commonly used for key exchange and digital signatures. By running the message through mathematical transformations defined by the algorithm, it becomes a randomized cipher that hides the original plaintext.
Examples of Cryptography Techniques
- Symmetric encryption: Plaintext is encrypted using a shared secret key, e.g. AES. It is faster but key distribution is an issue.
- Asymmetric encryption: Plaintext is encrypted with a public key but can only be decrypted with corresponding private key. Safer key exchange occurs via RSA, Diffie-Hellman.
- Digital signatures: A message is signed using a private key allowing anyone to verify authenticity with corresponding public key. Helps detect tampering via elliptic curve digital signature algorithm (ECDSA).
- Hashing: Cryptographic hash functions like SHA process input to produce a fixed-length hash value fingerprinting the original message. Useful for integrity checks and password storage instead of plaintext.
- Steganography: Hiding secret messages within other files like images to evade detection, different from encryption which scrambles information. Limited security however.
These methods enhance various aspects of secure transmission from confidentiality to authentication to non-repudiation through technical means rather than organizational policies alone.
The Hash Function
A hash function takes an input of any size and converts it into a fixed length output known as the hash value or hash code. Regular hash functions aim to provide a uniformly random distribution of outputs while spreading inputs evenly across that output range.
However cryptographic hash functions have an additional goal of being one-way functions that are practically impossible to invert. Given a hash, it must be computationally infeasible to find any input that generates that hash or to determine anything about the original message. This one-way property allows detecting even minute changes to hashed data with high probability.
Conversion of Data into an Encrypted String of Fixed Length
Plaintext inputs of any size like documents, passwords or transaction contents are compressed into numbers of a standard size determined by the hash algorithm, for example 256 bits for SHA-256. This fixed-length hash value acts like a digital signature or fingerprint for the input.
Hashing cuts down data while maintaining a strong semblance to the original information. Even minute changes like altering a single character in a long plaintext will vastly change the hash to an entirely different output cipher. This sensitivity is crucial for integrity checks when transmitting or storing hashed inputs.
Production of Unique Output that Cannot be Reverse-Engineered
A well-designed cryptographic hash will distribute results uniformly randomly across the output range such that finding collisions or pre-images requires brute-force attempts. It should be mathematically impossible given today’s computing capabilities to deduce the input even having its hash or to generate a specific target hash.
This one-way property prevents using hash outputs to replicate, forge or steal hashed entities like passwords, documents or blockchain transactions, instead requiring access to the secure plaintext original or key. It also makes cryptographic hashes well-suited for fingerprinting inputs.
Various Types of Hash Algorithms and their Output Lengths
Common hashing algorithms include MD5 (128-bit), SHA-1 (160-bit), SHA-2 family like SHA-256 and SHA-512 (256 to 512-bit), Whirlpool (512-bit) among others. Each has different strengths and weaknesses but are designed to make guessing inputs or generating collisions infeasible with hash pre-image resistance and second pre-image resistance properties.
Longer hash lengths provide improved security margins against theoretical attacks like length extension but impact performance. Selection depends on specific application balancing security, reliability and computational efficiency based on sensitivity of hashed data.
How Cryptographic Hash Functions Work
The main goal of cryptographic hash functions is to secure user data by protecting integrity and authentication through this hashing process. When a user submits personal information like their name, address or credit card details online, that data needs to be protected from snooping eyes or alteration during transmission and storage.
A cryptographic hash is generated from the input and compared at the receiving end to verify no changes occurred. This prevents malicious modifications without access to the original plaintext.
Common Use Cases of Hash Functions in Computing Systems
Cryptographic hashes see widespread usage in IT security:
- Data integrity checks by verifying stored or transmitted files against original hashed versions.
- Password storage using a hash+salt of credentials rather than plaintext for login authentication.
- Digital signatures via hashes of message content along with sender private key for verifiable authentication.
- Malware detection databases maintain hashes of known viruses for rapid scanning of new files.
- Watermarking or signatures for digital media through embedded invisible hashes within image/audio/video files.
- Blockchain technology secures transactions through chained hashing of prior blocks in distributed ledgers like Bitcoin.
- Code and document integration tracking via hash comparison during software/technical changes.
This diversity underscores the necessity of cryptographic hashes functioning as cryptographically secure checksums.
Differentiating Cryptographic Hash Functions from Regular Hash Functions
Regular (non-cryptographic) hash functions focus on efficiently mapping inputs to evenly-distributed outputs through collision-resistant hashing alone. Cryptographic variants add pre-image and second-pre-image resistance properties making it difficult given any hash output to determine input or generate a new input with that same hash value.
They are also specially designed to resist length extension attacks where an attacker can append data to an input and continue to hash that new string to guess later parts of a hash chain. Cryptographic security margins ensure outputs do not leak information about original messages.
Security Features Added by Cryptographic Hash Functions
Beyond uniform distribution and collision avoidance, cryptographic hashes incorporate deliberate complexity through techniques like mixing message bit strings and manipulating operational procedures during compression.
Additionally, cryptographically strong PRNGs initialize internal hash function variables to create more chaotic behaviors. Multiple execution rounds using internal hash iteration boost effective strength over a single function call.
Together these intricacies thwart efforts to discern input-output relationships, construct collisions or modify inputs without knowledge of the original plaintext. That enhanced protection from both external and insider threats earns cryptographic hashes trust for integrity-critical systems.
Properties of Cryptographic Hash Functions
Here are the key properties of cryptographic hash functions:
Collision-Free Property: No Two Inputs Should Map to the Same Output Hash
A cryptographic hash algorithm strives to distribute results across the finite output range randomly yet uniformly. It should be overwhelmingly difficult despite exhaustive searching to find any pair of messages that hash to the same value.
This property prevents substituting one input for another when using a hash for identification purposes. Even changing a single bit in different messages is likely to cause divergent outputs thanks to the avalanche effect making collisions effectively implausible.
Hidden Property: Difficulty in Guessing the Input Value from the Output
Given only a hash output, it must be computationally infeasible to deduce any characteristics of the original message such as its contents or length. The mapping from input to compressed hash value irreversibly discards message details using cryptographically secure one-way transformation.
Ideally the only approach is a brute force search of possible inputs, but the search space exponentially increases with larger inputs or output sizes beyond modern computational resources. This hinders tracing hashes to copied or altered messages.
Puzzle-Friendly Property: Difficulty in Selecting an Input That Produces a Specific Output
While regular hashes make finding inputs for a target hash trivial, cryptographic hashes should resist pre-image attacks with the goal hash value. Unless through exhaustive trial-and-error guesses, determining a message to yield a particular hash string represents an insurmountable challenge.
Applications like password storage therefore cannot support guessing passwords from only their hashes. Even partial knowledge of the input should not practically help narrow options for the remainder. Intentional complexity deters efforts to construct matching inputs.
4 Characteristics of a Strong Hash Function
A strong hash function possesses several important characteristics that make it reliable and secure. Here are brief explanations of four such characteristics:
1. Pre-image Resistance: A hash function exhibits pre-image resistance when it is computationally infeasible to determine the original input (pre-image) from the hash value. In other words, given a hash, it should be extremely difficult to find any input that would produce that specific hash. This property ensures that the hash function provides a one-way function, making it difficult to reverse-engineer the original data.
2. Avalanche Effect: The avalanche effect refers to the property where a slight change in the input of a hash function produces a drastically different output (hash value). Even a minor alteration in the input should result in a significant change in the resulting hash. This property ensures that even small modifications to the input will generate completely different hash values, making it difficult to find patterns or predict the output based on the input.
3. Collision Resistance: Collision resistance implies that it is highly improbable for two different inputs to produce the same hash value. In other words, it is computationally infeasible to find two distinct inputs that result in an identical hash. A strong hash function should minimize the likelihood of collisions, which helps in maintaining data integrity and enhances the security of cryptographic applications.
4. Deterministic Nature: A hash function is deterministic if it consistently produces the same output (hash) for the same input. This property ensures that given the same input, the hash function will always generate the same hash value. Determinism is crucial for various applications, including data integrity checks, password hashing, and digital signatures, as it enables verification and comparison of hash values.
Examples of Cryptographic Hash Functions
Blockchain technologies powering cryptocurrencies intrinsically rely on cryptographic hashing. Each block contains a hash referencing the previous block, chained together forming a permanent append-only transaction record.
Miners compete to be the first to find a hash for their block with a specific number of leading zeros. This proof-of-work secures the network through investment of computational resources. Tampering with older blocks means re-hashing the entire chain due to hash dependencies, safeguarding credibility of the distributed ledger.
Other Applications
Password databases store only salted hash + pepper formats of credentials. During login, entered values hash to compare equality against stored versions without ever exposing plaintext passwords. Digital signatures use private keys to sign document hashes for verifying authentic, untampered content and sender identity via public keys.
Hashing files before transfer or storage then comparing afterwards detects any alterations, as even minor changes yield unlikely hash collisions. Businesses may watermark multimedia content with invisible hashes tracing copies back to original owners.
Examples of Hash Function Outputs Using Different Algorithms
For the input string “Hello World”, sample hash outputs include:
- MD5: 5eb63bbbe01eeed093cb22bb8f5acdc3
- SHA-1: aaf4c61ddcc5e8a2dabede0f3b482cd9aea9434d
- SHA-256: 2cf24dba5fb0a30e26e83b2ac5b9e29e1b161e5c1fa7425e73043362938b9824
- Whirlpool: f7cc30e4d804a1276e8c3a2b54a219168d59deac39f67dd6da1963788fa1263d85d0c12645424f24e789a50d80dbf89d
Presenting sample hashes using different algorithms illustrates generally diverse yet predictable deterministic outputs for a known input.
Secure Hash Algorithm (SHA)
SHA (Secure Hash Algorithm) refers to a family of standardized cryptographic hash functions published by the National Institute of Standards and Technology (NIST) and the NSA. Some notable versions include:
- SHA-1 (160 bits) – Was widely used but no longer considered secure due to theoretical attacks finding collisions.
- SHA-2 family – Includes SHA-224, SHA-256, SHA-384, SHA-512 with outputs of 224 to 512 bits. Widely adopted as more secure replacements for SHA-1.
- SHA-3 – Keccak algorithm selected winner of NIST hash function competition in 2012, addresses theoretical weaknesses in earlier versions.
Segregation and Hashing of Data Blocks
All SHA versions operate similarly – the message is split into equally sized blocks which are processed in sequence. Each block’s hash becomes input for the next round along with new message bits. This chaining hides block boundaries and strengthens security.
Correlation Between Hashed Blocks
Dependency between block hashes discourages parallelization that could optimize pre-image attacks. Result uniqueness comes from mixing in previous computation results, not just the current block in isolation per round thanks to chaining.
Detection of Tampering through Changes in the Output
Even altering a single bit flips avalanche effects through cascaded rounds, yielding a radically different hash with high probability. Facilitates integrity checks by verifying pre-transmission hashes against received or stored versions.
Comparison of SHA-512 with Other Secure Hashing Algorithms
SHA-512 outputs 128 hex digits (512 bits). Offers security margins beyond foreseeable advances while maintaining performance. Preferable to SHA-1 or weaker hashes no longer considered secure against theoretical attacks. But may see SHA-3 gain broader adoption over time depending on post-quantum developments.
Theoretical Security and Practical Considerations of Using SHA-512
NIST analysis estimates SHA-512 requires a 2^512 operation brute force search to find collisions, well beyond capabilities. No meaningful attacks reported against properly implemented SHA-2 including SHA-512 to date. Continued use expected securely into foreseeable future barring unforeseen theoretical insights drastically reducing known lower security bounds. Overall a reliable, well-vetted choice.
Conclusion
In summary, cryptographic hash functions provide fundamental cryptographic services through their mathematical properties of one-wayness, collision resistance and input obscurity. Their fixed-length output fingerprints act as secure checksums for verifying data integrity whenever transmitting, storing or processing files and messages digitally.
Whether authenticating transactions on blockchains, checking downloaded software installations or securing password authentication systems, cryptographic hashes underpin a broad range of security protocols by deterministically yet unpredictably binding inputs to outputs. Their application of complexity tuned specifically against reversal, collisions and partial hashes has kept pace with growing computational abilities to remain viable defenses.
