By Giulia Traverso, Denise Demirel, Johannes Buchmann
Homomorphic signature schemes are a huge primitive for plenty of purposes and because their creation quite a few ideas were awarded. hence, during this paintings we offer the 1st exhaustive, whole, and up to date survey concerning the cutting-edge of homomorphic signature schemes. First, the overall framework the place homomorphic signatures are outlined is defined and it truly is proven how the presently on hand forms of homomorphic signatures can then be derived from any such framework. moreover, this paintings additionally provides an outline of every of the schemes awarded to date including the homes it offers. moreover, 3 use situations, digital vote casting, shrewdpermanent grids, and digital overall healthiness documents, the place homomorphic signature schemes should be hired are defined. for every of those purposes the necessities homomorphic signature scheme should still satisfy are outlined and the proper schemes already on hand are indexed. This additionally highlights the shortcomings of present recommendations. hence, this paintings concludes with a number of principles for destiny study towards homomorphic signature schemes.
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Additional resources for Homomorphic Signature Schemes: A Survey
F;iF / is given to A. 4) Steps 3)–4) are repeated for a polynomial number of times. The only constraint is that at most N messages can be queried for each filename F. 5) The adversary A outputs a tuple . ; m ; ; f /. Before concluding with Step 6) and stating how the attacker A wins, the following definition is introduced . 18. 17, a function f W M N ! miFC1 ; miFC2 ; : : : ; mN / 2 M N iF , where MF is the tuple of messages m queried for the filename F, listed in the order they were requested.
Another important feature of this scheme is that the length of the vector to be signed is unbounded. 4 Improved Security for Linearly Homomorphic Signatures: A Generic Framework, by Freeman  Besides the schemes described in Sect. 5, the generic framework presented in  also shows how to adapt two RSA-based signature schemes such that they support linear operations. More precisely, the scheme proposed in  relying on the Strong RSA assumption and the scheme proposed in  relying on the Standard RSA assumption are transformed.
Note that the first step in the verification algorithms depends on how the verification of the respective non-homomorphic scheme is performed. In the nonhomomorphic signature scheme presented in , there are three pairings in the verification algorithm, while in the non-homomorphic signature scheme described in  there are two pairings. g1 ; g2 /, which is computed at the initialization time once for all and then cached. We can then assume that the number of pairings are one for the scheme presented in  and two for the scheme introduced in .