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First we revisit three (BGLS, MBGLS and GZZ) verifiably encrypted signature schemes. We find that they are all not strong unforgeable. We remark that the notion of existential unforgeable is not sufficient for fair exchange protocols in most circumstances. So we propose three new (NBGLS, MBGLS and NGZZ) verifiably encrypted signature schemes which are strong unforgeable. Also we reconsider other two...