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Many cryptographic applications of hash functions are analyzed in the random oracle model. Unfortunately, most concrete hash functions, including the SHA family, use the iterative (Strengthened) Merkle-Damg?ard transform applied to a corresponding compression function. Moreover, it is well known that the resulting "Structured" hash function cannot be generically used as a random oracle, even if the compression function is assumed to be ideal. This leaves a large disconnect between theory and practice: although no attack is known for many concrete applications utilizing existing (Merkle-Damg?ard based) hash functions, there is no security guarantee either, even by idealizing the compression function.
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