Full Domain Hash - Alchetron, The Free Social Encyclopedia

In cryptography, the Full Domain Hash (FDH) is an RSA-based signature scheme that follows the hash-and-sign paradigm. It is provably secure (i.e., is existentially unforgeable under adaptive chosen-message attacks) in the random oracle model. FDH involves hashing a message using a function whose image size equals the size of the RSA modulus, and then raising the result to the secret RSA exponent.

Exact security of full domain hash

In the random oracle model, if RSA is ( t ′ , ϵ ′ ) -secure, then the full domain hash RSA signature scheme is ( t , ϵ ) -secure where,

t = t ′ − ( q hash + q sig + 1 ) ⋅ O ( k 3 ) ϵ = ( 1 + 1 q sig ) q sig + 1 ⋅ q sig ⋅ ϵ ′ .

For large q sig this boils down to ϵ ∼ exp ⁡ ( 1 ) ⋅ q sig ⋅ ϵ ′ .

This means that if there exists an algorithm that can forge a new FDH signature that runs in time t, computes at most q hash hashes, asks for at most q sig signatures and succeeds with probability ϵ , then there must also exist an algorithm that breaks RSA with probability ϵ ′ in time t ′ .

References

Full Domain Hash Wikipedia

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