Hashing scheme

Geometric hashing73 originated from the area of computer vision and was first applied to molecular docking problems by Fischer et al.74,75 In computer vision, the geometric hashing scheme was developed for the problem of recognizing (partially occluded) objects in camera scenes. In principle,... 

Figure 2 Simple illustration of bit string encoding of chemical structure, (a) Sample of a fragment dictionary-based approach, (b) Sample of a hashing scheme using a path-based decomposition of the structure. The asterisk denotes an element in the bit string where a collision has resulted from the hashing procedure.

Most full-structure search systems use a hashing scheme to quickly locate potential matches and then perform a full lexical comparison of the name. A hashing function is used that takes the canonical name as input and returns a disk location to store and retrieve the name from. The number of hash collisions (where two different structures have the same hash value) is dependent on the hash function used and percentage utilization of the hash space. This database access method means that search speeds are relatively independent of database size, except where excessive hash collisions occur or numerous matches occur. 

The Hash thermolysis of the dioxolene (124) gave diphenylketene among the products (Scheme 107) (70CC206), and it is conceivable that diphenyloxirene is the precursor of this product. 

This scheme is introduced in [4, 8], and also used in [7]. It differs from the basic scheme in the preprocessing and hiding operations. A secure hash function is applied to the signature before embedding, in order to reduce its size. The locations of the embedded CLBs are also fingerprinted with the identity of the user in order to trace back the origin of mis-appropriation. Additional hiding operations are also put in. 

The formation of cyclic nitrones (150) from pericyclic mechanism. Kinetic and computational studies have provided evidence for the involvement of a novel pseudo-pericyclic electrocyclization in the conversion of o-vinylphenyl isocyanates into quinolin-2-ones. " Such reactions have also provided evidence of torquoselectivity in a 6jt system. Hash vacuum thermolysis of triazoles (151) has been found to afford dihydroquinolines (155), presumably by generation of a-oxoketenimines (152) which can undergo a [1,5]-hydrogen shift to the o-quinoid imines (153)7(154) and subsequent electrocyclization (see Scheme 57). 

Lamdan, Y., Woleson, H. J. Geometric Hashing a general and efficient model-based recognition scheme. 

Scheme 2. Overview of NB and NSB hydrogenation (hashed lines denote multiple surface steps).

Computer Vision, 1988, pp. 238-249. Geometric Hashing A General and Efficient Model-Based Recognition Scheme. 

As an alternative to completely enumerating all relative orientations, Fischer et al.52 reported the development of a computer-vision-based technique called geometric hashing. This scheme is conceptually similar to that utilized in the DOCK program53,74 which tries to find matches in the internal distances between spheres74 or shape-based site-points,53 which represent the surface features of the proteins. 

In more or less this form, and with one-way and hash functions of high efficiency, but unproven security, the scheme is nowadays still being considered for practical applications [Merk88, MeMa82 pp. 396-409, Meye91, Vaud92, BlMa94]. 

More generally, the proposed schemes with redundancy or fast hash functions (often based on symmetric cryptologic schemes such as DBS) have a rather chaotic overall structure, so that one cannot even hope that breaking them is equivalent to a well-examined problem such as factoring. 

The first major step was to recognize that redundancy or hash functions are not some protocol around the real signature scheme. Instead, the signature scheme must comprise everything that happens with the message, and security must be proved for this complete scheme. 

The complexity of the most efficient schemes for signing one message block is almost as low as that of efficient ordinary digital signature schemes. The same holds if message hashing is added. (Note that this subsection assumes a fixed risk bearer or any other version that has the same effect on the efficiency of authentication, cf. Figure 6.2.)... 

If one considers all schemes that look moderately secure, such as RSA with the additional measures described in Section 2.5, ordinary digital signature schemes exist where the complexity of one authentication is independent of the overall number of messages to be authenticated. In this case, one usually decides to trust fast hash functions, too, so that long messages can be signed fast. 

If one uses such a fast hash function in bottom-up tree authentication for a fail-stop signature scheme, the overhead for the tree part (for trees of reasonable size, such as depth 20) is small in comparison with the actual signature, at least in time complexity. (This is why one-time signature schemes with tree authentication are still considered in practice, see Section 2.4.)... 

Note that a weaker notion of families of hash functions exists, too, so-called families of universal one-way hash functions [NaYu89]. However, in the applications to fail-stop signature schemes, collision-intractability is needed. 

Now tuple exponentiation is turned into collision-intractable families of fixed-size hash functions. This was first done in [ChHP92] the construction was extended for the use in incremental signature schemes in [BeGG94]. In particular, one can use pair exponentiation, but larger tuples tiun out to be more efficient. 

If one combines message hashing with fail-stop signature schemes, the following conditions have to be fulfilled ... 

The key for the family of hash functions, i.e., the description of the particular function used, must be chosen by the risk bearer s entity (because collision-intractability is only guaranteed against parties who did not generate this key). Hence in schemes with prekey, this key is a part of the prekey. 

The parameters must be chosen so that each hash value is an element of the message-block space of the underlying signature scheme. In general, this makes parameter transformations similar to Construction 8.50 necessary. 

In the following, first a general theorem about combinations of hash functions and standard fail-stop signature schemes with prekey is presented formally. If a concrete fail-stop signature scheme based on a factoring or discrete-logarithm assumption is used, it is natural to combine it with a family of hash functions based on the same assumption. These special cases are considered afterwards. 

A family of embeddings of the codomains of the hash functions into message-block spaces of the signature scheme, i.e., a family of injective functions... 

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