Excerpt
Hash collisions are possible in any function. This post explains what causes them, risks involved, and strategies to mitigate collision issues.
Hashing is an essential concept in computer science and cryptography. It involves generating a fixed-size string or number from a variable-sized input using a hash function. Hashing plays a crucial role in various applications like data integrity checks, digital signatures, password storage, and database lookup. A pertinent question that arises is - can two different inputs produce the same hash output? This blog post dives into the causes and implications of such hash collisions.
What is a hash function?
A hash function is a mathematical algorithm that maps data of arbitrary size to a fixed-size value called a hash value or hash. Some common examples include MD5, SHA-1, SHA-256, etc.
The purpose of a hash function is to quickly generate a small digital fingerprint for any input. This enables easy comparison and identification of the original data. For instance, a hash can be used to generate a fingerprint for a password to store it securely instead of the plain text password.
How does a hash function work?
A hash function applies certain mathematical operations like modular arithmetic on the input message to produce a hash value. Here are the typical steps:
The input data is broken down into chunks of equal size.
These chunks are concatenated together.
Padding may be added to meet the required bit size.
The padded input is broken into blocks of 512 bits each.
The hash algorithm performs several rounds of mathematical operations on each block. Common operations include bit shifting, modulo arithmetic, XORing, etc.
The output of each block is combined using a compression function to generate the final hash value.
For example, to hash the input string “IToolkit” using the SHA256 algorithm:
1// Input
2string input = "IToolkit";
3
4// Step 1. Break into chunks
5char[] chars = input.ToCharArray();
6
7// Step 2. Concatenate
8string concatenated = new String(chars);
9
10// Step 3. Apply padding
11string padded = Concatenate(concatenated, padding);
12
13// Step 4. Break into 512 bit blocks
14int numBlocks = padded.Length/512;
15byte[][] blocks = new byte[numBlocks][];
16
17// Step 5. Apply hash algorithm
18byte[] hashBytes = SHA256(blocks);
19
20// Step 6. Get hex string
21string hash = HexEncode(hashBytes);
22
23// Sample output:
24// a605964b68ca0c9a2e5d6d60bad205e50da78691d7821137df82d33affde577e
This results in a fixed length 256-bit (64 character) hash value for any arbitrary length input.
Can one hash output be for different inputs?
In an ideal hash function, each input should map to a completely unique hash output. However, since hash functions produce hashes of a fixed length, there is a possibility of two different inputs producing the same output hash. This is known as a hash collision.
Such collisions are practically unavoidable in any hash function. But a good cryptographic hash aims to minimize the chances of collisions to improve security.
Hash collisions have been found in widely used functions like MD5, SHA-1, etc. In 2005, researchers found techniques to generate SHA-1 collisions reliably. This led to agencies like NIST declaring it insecure for digital signatures.
Here I will provide you with a free online hash verification tool, come and try it.
Factors affecting hash collisions
The likelihood of collisions depends on:
Size of inputs - Longer inputs have a greater chance of collision. There are limited possible hashes, so more inputs increase chances of clashing.
Output size - More output bits means more possible hash values. So 256-bit SHA256 has lower collisions than 128-bit MD5.
Hash function design - A high-quality hash like SHA256 is engineered to minimize collisions. Weak algorithms like MD5 have higher chances.
According to the birthday problem in probability, once you have √(n) inputs, there is over 50% chance of a collision where n is number of possible hashes.
Implications of hash collisions
Hash collisions can undermine certain security assumptions and have implications in applications like:
Digital signatures - A collision would allow an attacker to swap the signed document while retaining the same signature.
Password storage - Identical hashes for different passwords mean an attacker could log in using other passwords in the database.
File identifiers - Colliding file hashes can cause misidentification of downloaded files and version mixups.
Blockchain - Mining valid blocks with colliding hashes affects consensus and allows double spending.
Therefore, mission critical systems need to rely on collision-resistant hash functions like SHA256. Weak hash algorithms should not be used in sensitive contexts.
Techniques to mitigate hash collisions
Here are some strategies to reduce the risks associated with hash collisions:
Use well-studied cryptographic hash functions like SHA-256, SHA-3, etc. that are extremely resistant to collisions.
For passwords, add salts to introduce randomness before hashing to prevent same outputs.
Where needed, use larger hash outputs like SHA-512 to lower collision chances.
In hash tables, handle collisions using chaining or probing to store colliding entries.
For files, store additional metadata like size to detect changed content with the same hash.
When collisions occur, have a defined collision resolution plan to handle incidents and prevent exploitation.
Conclusion
Hash collisions are a possibility in any hash function, but good algorithms like SHA-256 minimize this risk significantly. Understanding the causes and mitigation strategies allows developing secure systems resilient to hash collisions. Using strong modern hashing and adding salts, collision handling, and redundancy helps reduce the impacts in case collisions occur. Overall, being aware of the subtleties in hashing is key to leveraging their usefulness while avoiding pitfalls.
