Secondpreimage

Second preimage refers to a concept in cryptography related to hash functions. Given a hash function H and an input x, a second preimage is another input x' not equal to x such that H(x') = H(x). Second preimage resistance is the property that, for a randomly chosen hash function, it should be computationally infeasible to find such an x' when x is fixed.

This concept is distinct from preimage resistance, which asks for an input x that produces a given hash value y (H(x) = y), and from collision resistance, which asks for any two distinct inputs that hash to the same value. In second preimage analysis, the attacker targets a specific x; a successful attack would yield a different message with the same hash as the original, enabling forgery or tampering without altering the hash.

For an ideal n-bit hash function, second preimage resistance is expected to require about 2^n evaluations of H to find a valid x'. By contrast, finding any collision is easier, occurring with high probability around 2^(n/2) evaluations due to the birthday paradox. Thus, second preimage resistance is typically a stronger and more demanding property than collision resistance.

In practice, hash functions such as SHA-256 (256-bit output) are designed to provide strong second preimage resistance, though actual security depends on ongoing cryptanalysis; no practical second preimage attack is known for these designs. Second preimage resistance is important for maintaining integrity in digital signatures and data authentication.