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Have there ever been some publicized efforts to prevent length extension attacks of hashing algorithms that are based on the Merkle–Damgård construction (MD5, SHA1, SHA2, ...)?

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    $\begingroup$ Double-Hashing and truncation? $\endgroup$
    – SEJPM
    Apr 3 '19 at 13:05
  • $\begingroup$ HMAC is the typical construction $\endgroup$
    – Natanael
    Apr 4 '19 at 0:01
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Yes. In this paper, Coron and al. showed that a plain MD construction is secure when it's inputs are prefix-free. They actually proved the indifferentiability of the construction. In other words messages need to be encoded in a prefix-free manner.

Quoting the paper:

A prefix-free code over the alphabet $\{0, 1\}^κ$is an efficiently computable injective function $g: \{0, 1\}^∗ \to (\{0, 1\}^κ)^∗$such that for all $x \neq y$, $g(x)$ is not a prefix of $g(y)$.

One such encoding is given in the paper

Function g1(m): let $N$ be the message length of $m$ in bits. write $m$ as $(m_1, \ldots , m_l)$ where for all $i$, $|m_i| = k$. and with the last block $m_l$ padded with $10^r$. let $g1(m) = (\langle N \rangle, m_1, \ldots , m_l)$ where $\langle N \rangle$ is a $κ$-bit binary encoding of $N$.

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  • Fixed output filters like SHA-256d
  • Keyed output filters like HMAC, envelope-MAC, etc.
  • Truncation like SHA-512/256
  • Prefix-free message encoding like length-prefixed
  • Non-MD designs like BLAKE2 with HAIFA, SHA-3 with a sponge
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