Collision bundling homomorphisms

Definition S.30. A coliision-intractabie family of bundling homomorphisms is a collision-intractable family of bundling functions with the following additional properties and components ... 

After all the mathematical and computational preparations, it is quite clear that pair exponentiation in a family of groups of prime order where the discrete logarithm is hard yields a collision-intractable family of bundling homomorphisms. (It was first used in this way in [HePe93].) It only remains to be decided how the security parameters are related, because the family of groups has only one, k, whereas the family of bundling homomorphisms has two, say k and T for distinction. The following facts are known ... 

The following table summarizes the most important parameters of the constructions of collision-intractable families of bundling homomorphisms, hiding homomor-phisms, and fixed-size hash functions based on the discrete-logarithm assumption. Note that the main use of fixed-size hash functions is in the constmction of real hash functions. 

The construction of a collision-intractable family of bundling homomorphisms from iterated squaring and doubling is basically Construction 8.56, based on the claw-intractable families of permutation pairs from Construction 8.64. The new points are ... 

Theorem 8.67 (Iterated squaring and doubling as bundling homomor-phisms). On the factoring assumption. Construction 8.66 defines a collision-intractable family of bundling homomorphisms. ... 

In this section, a framework for constructing standard fail-stop signature schemes with prekey for signing one message block from a collision-intractable family of bundling homomorphisms is described. Two parameters (the exact family of... 

A collision-intractable family BundFam of bundling homomorphisms. The same... 

BundFam, the collision-intractable family of bundling homomorphisms, is given by Construction 8.44, i.e., pair exponentiation in the given family of groups. Its... 

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