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In this paper we describe a new identity-based signcryption (IBSC) scheme built upon bilinear maps. This scheme turns out to be more efficient than all others proposed so far. We prove its security in a formal model under recently studied computational assumptions and in the random oracle model. As a result of independent interest, we propose a new provably secure identity-based signature (IBS) scheme that is also faster than all known pairing-based IBS methods.