Abstract
In this chapter the state of the art with respect to homomorphic signature schemes is presented. Due to the large number and the different properties they satisfy, they are discussed in separate groups, according to the computations they support. The linearly homomorphic signature schemes are further divided with respect to the hardness assumption they rely on. Afterwards, the existing homomorphic signature schemes for polynomial functions and the fully homomorphic ones are described. Regarding the existing homomorphic signature schemes for the multi-users case, the linearly homomorphic aggregate signature schemes and the multiple sources linearly homomorphic signature schemes are presented separately. The investigated properties are the ones introduced in the previous section. For each scheme the underlying hardness assumption is specified, then we provide information about the efficiency of the schemes and their signature’s length. Afterwards, the general safety of the scheme is discussed: which adversary the signature can cope with and which level of privacy it achieves.
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