Birthday Attack Definition

A birthday attack is a way to find two different inputs that produce the same hash value, also called a collision. Attackers use this to trick systems that depend on hashes for integrity checks, digital signatures, or password storage. 

The idea: the birthday problem

The name comes from the birthday problem in probability. In a room of 23 people, there is about a 50 percent chance that two share a birthday. In hashing, the same math means collisions appear much sooner than simple intuition suggests, so testing many inputs quickly becomes effective. 

How a birthday attack works

An attacker picks a target hash function, then generates lots of slightly different inputs. These variations can be as small as adding spaces or punctuation. The attacker hashes each candidate and looks for any two that land on the same output. With a collision in hand, the attacker can swap a benign item for a malicious one that has the same hash and slip past a verification step. 

Why it works: the birthday bound

For a hash with an n-bit output, the work needed to find a collision is roughly 2^(n/2) trials, not 2^n. That “square-root” effect explains why short hash outputs are risky and why modern systems choose longer outputs. 

Where attacks show up

Collisions can break workflows that assume each hash is unique. Examples include tricking someone into signing one document while later substituting a different document with the same hash, and finding a different password that matches a stored password hash. These scenarios can lead to fraudulent approvals or unauthorized access. 

How to reduce the risk

Use strong, modern hash functions with long outputs, and avoid outdated ones. Add message authentication codes when verifying data in transit or storage. Keep crypto libraries updated so implementations follow current guidance. Longer outputs raise the collision bar, and MACs add an integrity check that resists simple collision tricks.

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