Abs t rac t . In this paper, we propose two efficient RSA multisignature schemes, one is an improved version of Okamoto's scheme [6] and the other is that of Kiesler-Harn's scheme [3]. The first one causes bit expansion in block size of a multisignature, but the bit length of the expansion is no more greater than the number of signers regardless of their RSA modulus. The second one has no bit expansion, in which all signers have a RSA modulus with the same bit size and the same most significant 1 bits pattern. An average number of the required exponentiations to obtain a multisignature is about (1 -b 2111 )m, where m denotes the number of signers. Futhermore, our schemes have no restriction in signing order and are claimed to be more efficient than Okamoto's scheme and Kiesler-Harn's scheme respectively.
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