Anshuman
Anshuman Singh
Senior Executive - Content
Updated on Jan 17, 2024 16:02 IST

In today's time, where data security is paramount, cryptographic attacks pose a significant threat to individuals and businesses. One such powerful attack is the birthday attack, which exploits the mathematics behind the birthday problem to find a collision in a hash function. 

Birthday Attack

This article will delve deeper into what a birthday attack is, how it works, and its impact on digital signatures and hash tables. We will also explore hypothetical examples of the birthday attack to help you comprehend better and discuss possible ways to mitigate its effects. 

Table of Content (TOC)

What is a Birthday Attack?

A birthday attack is a type of cryptographic attack that belongs to a class of brute-force attacks and exploits the mathematics behind the birthday problem (birthday paradox) to find a collision in a hash function. 

Birthday Paradox is a statistical phenomenon that reveals that in a group of just 23 people, there is a 50% chance that at least two of them share the same birthday.

In cryptography, a hash function is a mathematical function that takes an input (message) of any length and generates a fixed-size output called a hash or hash value. As per the hash function's design, getting the same hash value from two different input messages is highly unlikely. This property of the hash function is called collision resistance. But, as possible hash outputs are limited because of the hash function's design, collision will likely occur at some time. 

In a birthday attack, an attacker randomly generates many inputs (like messages) and calculates their hash values. Then, these values are stored in a table. As more values are generated, the probability of a collision (two different inputs with the same hash) increases rapidly, just like the birthday paradox. Once a collision is found, the attacker can exploit it in various ways, depending on the application.

What is a Salami Attack and How to protect against it?

Difference Between Active and Passive Attacks

Difference Between Hackers and Crackers
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Birthday Attack Example

For simplicity, let's use a hypothetical and simplified scenario.

Step 1: Understanding Hash Functions

  • Imagine a hash function that converts any input (like a word, sentence, etc.) into a fixed-size string of characters (hash). For instance, it might turn "Hello" into "1a79a4d60de6718e8e5b326e338ae533".

Step 2: The Goal of the Attack

  • The attacker aims to find two different inputs that produce the same hash output. For example, finding two different sentences that produce the exact same hash when put through the hash function.

Step 3: Generating Inputs

  • The attacker starts generating a large number of different inputs. These could be random strings of text, numbers, or any data that can be hashed.

Step 4: Hashing Each Input

  • Each of these inputs is put through the hash function. The attacker keeps track of the resulting hashes. For instance, "Apple" might hash to "b2f5ff47436671b6e533d8dc3614845d" and "Orange" to "e8ef7b9cfeedc9f9b4b4f7b08a7ea5f5".

Step 5: Looking for Matches

  • The attacker then looks for two inputs that result in the same hash. Due to the principles of the Birthday Paradox, this takes less time than one might expect. While many possible inputs exist, the number of possible hash outputs is limited (by the hash function's design), increasing the likelihood of a collision.

Step 6: Finding a Collision

  • Suppose, after many attempts, the attacker finds that both "Blue Sky" and "Green Grass" produce the same hash, say "d41d8cd98f00b204e9800998ecf8427e". This is a collision. The attacker has successfully completed a Birthday Attack.

Step 7: Exploiting the Collision

  • The attacker can use this knowledge to their advantage. For instance, if a system checks data integrity by comparing hash values, the attacker could replace "Blue Sky" with "Green Grass" without the system realizing the data has changed, as the hashes match.

Real-Life Cases of the Birthday Attack

  • SSL Certificates: In 2008, researchers demonstrated that they could create fraudulent SSL certificates using a birthday attack. They generated two certificates with the same hash value, one for a legitimate website and one for a malicious one. The attacker could then use the legitimate certificate to masquerade as a legitimate website and intercept sensitive information. 
  • MD5 Hashing: In 2004, a group of researchers discovered they could use the birthday attack to create two files with the same MD5 hash value. This meant that an attacker could create a malicious file with the same hash value as a legitimate file, making it difficult to detect the difference. 
  • Bitcoin: In 2013, researchers used the birthday attack to generate two different Bitcoin private keys with the same hash value. This allowed them to steal Bitcoins from a wallet by using one of the keys to sign a transaction and then replacing it with the other key, making it look like the transaction was valid.

Birthday Attack's Impact on Digital Signatures and Hash Tables

Digital Signatures

A digital signature acts as a cryptographic seal to verify the authenticity and integrity of a document. It works by hashing the document and encrypting the hash with the signer's private key. Anyone with the public key can then decrypt the signature and compare it to the document's hash. If they match, the document is authentic and hasn't been tampered with.

But by using a birthday attack, an attacker can exploit hash collisions to compromise this security in several ways:

  • Forgery: An attacker can create two documents with the same hash by slightly modifying the content (inserting spaces, synonyms, etc.). This allows them to attach the legitimate signature from one document to the malicious one, making it appear authentic.
  • Tampering: The attacker can modify a signed document or message without breaking the signature, potentially changing the document's meaning.
  • Repudiation: By creating a fraudulent document with a valid signature, the attacker can falsely claim that the other party (the signer) created it. This makes it challenging to prove who authored the document.
  • Key compromise: In some signature schemes, brute-force attacks using collisions can help discover the signer's private key, effectively granting complete control over future signatures.

Hash Tables

Hash tables are data structures that use hash functions to find and store key-value pairs. Collisions play a vital role here, as two different keys can map to the same bucket due to a shared hash value. This leads to several issues:

  • Performance degradation: When collisions occur, multiple key-value pairs must share the same bucket, leading to additional comparisons and slower lookup times.
  • Data corruption: If collisions aren't handled properly, data belonging to one key can overwrite or be obscured by data associated with another key, causing corruption and potential loss of information.
  • Denial-of-service attacks: An attacker can deliberately create numerous collisions to overflow the hash table, making it unusable for legitimate operations.

Difference Between DOS and DDOS Attack

How to Prevent Birthday Attack?

Here are some key strategies:

Larger Hash Function Outputs

The higher the number of bits in the hash function output, the more spread out and unique the hash values become. This significantly reduces the probability of collisions for a given number of inputs. Secure algorithms like SHA-256 and SHA-3 utilize larger output sizes, making them much less susceptible to birthday attacks than older algorithms like MD5.

Salting

Adding a random string (salt) to the input before hashing expands the output space for each potential input. Imagine it as sprinkling unique spices on your message before generating the hash-dish. Even two similar messages with the same ingredients (words) will taste (hash) differently due to the unique salt blend. This further decreases the likelihood of collisions and adds an extra layer of protection.

Secure Hash Table Implementations

Collision-resistant hash functions are crucial for hash tables, but additional strategies can also enhance security. Techniques like separate chaining or cuckoo hashing effectively manage collisions by allocating separate "buckets" or dynamically re-adjusting key placements to minimize performance impact and data corruption.

Continuous Monitoring and Evaluation

Regularly monitoring systems for signs of malicious activity and evaluating the suitability of cryptographic algorithms for evolving threats is crucial. As computational power increases, what was once secure might become vulnerable, so adapting and upgrading defences is essential.

Utilize Keyed Hash Functions

A keyed hash function, like HMAC-SHA256, KMAC, BLAKE2b, and BLAKE3, incorporates a secret key into the hash process. In this method, the hash is generated based on the input data and a secret key. This means that even if an attacker can generate two inputs that produce the same hash, they still need the secret key to generate the valid hash values the system recognizes. This adds a layer of complexity and security.

Utilize Multiple Hash Functions

This approach involves using more than one hash function to generate multiple hashes for the same data. The idea is that finding a collision would require the attacker to find inputs that simultaneously collide across all used hash functions, which is significantly more difficult. 

For instance, if a system uses two different hash functions (SHA-256 and SHA-3), an input must produce the same hash output under both functions to be considered a collision. The likelihood of this happening is drastically lower than a collision in a single hash function.

About the Author
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Anshuman Singh
Senior Executive - Content

Anshuman Singh is an accomplished content writer with over three years of experience specializing in cybersecurity, cloud computing, networking, and software testing. Known for his clear, concise, and informative wr... Read Full Bio