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Differential uniformity is an important property of cryptographic building blocks used in the design of symmetric ciphers. In this paper it is proved that certain canonical mappings on elliptic curves are differentially uniform. The main observation of this paper is that the impersonation attack against the implicit certificate scheme of Ateniese and de Medeiros does not work if a differentially uniform mapping is used in the scheme. This phenomenon is analyzed in the slightly more general context of a partially blind signature scheme, which is a new cryptographic primitive that seems to gain security properties from differentially uniform mappings.