# State of research on SHA-1 Collision Attacks

SHA-1 security has been discussed since an algorithm for finding collisions was first published at CRYPTO 2004 and has been subsequently improved.

Wikipedia lists a couple of references, however it seems the latest research published (and later withdrawn) on this subject was in 2009 (Cameron McDonald, Philip Hawkes and Josef Pieprzyk "Differential Path for SHA-1 with complexity O(2^52)").

Since then, has any significant progress been made on reducing the effort for a hash collision attack on SHA-1?

A link to specific research accompanied with a short summary would be appreciated.

It is an identical-prefix collision attack that enabled the attacker to forge two distinct PDF documents that have the same SHA-1 hash value. I.e. They extended a given prefix $$p$$ with two distinct near-collision block pairs for any suffix $$s$$ that collides.
$$\operatorname{SHA-1}(p \mathbin\Vert m_0 \mathbin\Vert m_1 \mathbin\Vert s) = \operatorname{SHA-1}(p \mathbin\Vert m'_0 \mathbin\Vert m'_1 \mathbin\Vert s)$$ for any suffix $$s$$, where $$(m_0, m_1) \neq (m'_0, m'_1)$$
The computational requirement is estimated to $$2^{63.1}$$