Can You Break a Hash?

Hash functions, like SHA-1, are essential in cryptography and digital security, designed to convert data into a fixed-length “digest.” This process is meant to be one-way, meaning you can’t easily retrieve the original data from the hash. While this sounds secure, history has shown us that even the strongest algorithms can be compromised. But how do these hash functions get broken?

Let’s break it down by exploring how attacks on hash functions unfold and why they matter in modern cryptography.

1. Collisions: When Two Worlds Collide

At the heart of many hash function vulnerabilities lies a phenomenon called a collision. A collision occurs when two different inputs produce the same hash output. Since hash outputs are of fixed length (e.g., 256 bits for SHA-256), but the possible inputs are infinite, the math guarantees that some inputs will share the same hash. When attackers discover a collision, they’ve found a weak spot in the hash function.

How collisions break a hash:

Imagine downloading a piece of software, and the integrity of the file is verified by its hash. If an attacker can generate a malicious version of the software that produces the same hash as the legitimate one, they can trick the system into accepting the corrupted file.

Why this is dangerous:

A collision can allow attackers to substitute legitimate data with malicious data without detection. This is exactly what happened with SHA-1 in 2017, when researchers found two different PDF files that shared the same SHA-1 hash, effectively “breaking” SHA-1’s security.

2. Brute Force Attacks: Testing Every Key in the Lock

A brute force attack is exactly what it sounds like — attackers try every possible input until they find one that produces the desired hash. Theoretically, brute force could uncover the original input for a hash or create a collision, but in practice, this is incredibly hard due to the sheer number of possibilities.

Why this is difficult:

For modern hashes like SHA-256, the number of possible outputs is enormous — around 2²⁵⁶ different hashes. Even with today’s fastest computers, trying every possible input could take millions of years. However, this doesn’t mean brute force attacks aren’t a threat.

Why it still matters:

As computing technology advances — especially with the rise of quantum computing — brute force attacks could eventually become faster. Today’s secure hash functions might not be secure tomorrow, as faster computing makes brute force more feasible.

3. Cryptanalysis: Cracking the Math

Cryptanalysis refers to sophisticated techniques that examine the internal workings of a hash function to find mathematical weaknesses. These techniques reduce the effort needed to find collisions or reverse a hash.

Example:

SHA-1’s downfall came when researchers used advanced cryptanalysis techniques to significantly reduce the computational effort required to find a collision. In 2017, the SHAttered attack demonstrated a practical collision for SHA-1, showing that it was no longer safe for critical applications.

4. Birthday Attacks: A Surprising Shortcut

The birthday paradox — the counterintuitive probability theory that in a group of 23 people, there’s a better-than-even chance two will share the same birthday — also applies to hash functions. A birthday attack takes advantage of this math to find a collision faster than you’d expect.

How it works:

Instead of trying to match a specific hash, the attacker only needs to find any two inputs that produce the same hash. The birthday paradox makes it easier to find a collision than to reverse the hash or find a specific collision.

Why it matters:

The probability of a collision is higher than one might think, making it a practical approach for attackers. With enough computational power, a birthday attack can lead to serious vulnerabilities, especially in weaker hash functions.

5. Pre-image and Second Pre-image Attacks: The Search for the Original

Two additional types of attacks, pre-image and second pre-image attacks, also threaten hash functions.

• Pre-image attack: Given a hash, an attacker tries to find the original input that created it. This is extremely hard for secure hash functions, but advancements in cryptanalysis could make it more feasible.
• Second pre-image attack: Given a specific input and its hash, an attacker tries to find another input that produces the same hash. This is also difficult, but like all security measures, it depends on the strength of the hash function in question.

The End of SHA-1: How Researchers Cracked It

SHA-1 was once considered a secure hash function, but its fall began in 2017 with a method called SHAttered. Researchers from Google and CWI Amsterdam generated two different PDF files with the same SHA-1 hash, showing the world that SHA-1 could no longer be trusted.

The scale of the attack:

This collision required a staggering amount of computational power — over 6,500 years of CPU computation — but the fact that it was possible meant that SHA-1 was no longer secure for real-world applications. The once-robust algorithm had been mathematically “broken.”

What the Future Holds for Hash Functions

No hash function is unbreakable, but they are designed to be extremely difficult to break using current computing power. However, over time:

• Advances in computing (such as quantum computing) make it possible to find collisions or reverse hashes faster than expected.
• Weaknesses in hash functions’ designs (like SHA-1) can be exploited by attackers through techniques like cryptanalysis or birthday attacks.

This is why cryptographic communities have already moved from SHA-1 to newer, stronger algorithms like SHA-2 and SHA-3. As computing power grows and techniques evolve, the field of cryptography must continually adapt to stay ahead of potential attackers.