Concatenation of Cryptographic Hash Functions
Concatenating outputs from multiple hash functions provides collision resistance as good as the strongest of the algorithms included in the concatenated result. For example, older versions of TLS/SSL use concatenated MD5 and SHA-1 sums; that ensures that a method to find collisions in one of the functions doesn't allow forging traffic protected with both functions.
For Merkle-Damgård hash functions, the concatenated function is as collision-resistant as its strongest component, but not more collision-resistant. Joux noted that 2-collisions lead to n-collisions: if it is feasible to find two messages with the same MD5 hash, it is effectively no more difficult to find as many messages as the attacker desires with identical MD5 hashes. Among the n messages with the same MD5 hash, there is likely to be a collision in SHA-1. The additional work needed to find the SHA-1 collision (beyond the exponential birthday search) is polynomial. This argument is summarized by Finney. A more current paper and full proof of the security of such a combined construction gives a clearer and more complete explanation of the above.
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