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Understanding Security

In the Understanding Hashes section, I explain what preimage resistance, second-preimage resistance, and collision resistance mean. In this section, I show what these properties say in practice — and where their limits lie.

  • The Birthday Paradox Explains why, with 23 people, there is already a probability of around 50.7 percent that two of them share a birthday, and why the same effect limits the collision security of an ideal hash to roughly 2^(n/2).

  • How Does a Birthday Attack Work? Explains how the birthday effect can be used for a generic collision search, and why a birthday attack is neither a preimage attack nor a second-preimage attack.

  • How Secure Are 128, 256, and 512 Bits? Explains what security strength means, why hash length and collision security are not the same thing, and why cryptographic bit figures grow exponentially.

  • Can You Reverse a Hash? Explains why hashes cannot be decrypted, and why attackers can still find matching inputs when the input space is small or predictable.