| Summary: | This paper presents multi-user protocol-extensions for Schnoff/Nyberg-Ruepple (NR) signatures and Zheng signcryption, both of which are elliptic curve (EC)/discrete logarithmic (DL) formulations. Our extension methodology is based on k-of-n threshold cryptography-with Shamir polynomial parameterisation and Feldman-Pedersen verification-resulting in multi-sender Schnorr-NR (SNR) and multi-sender/receiver Zheng-NR (ZNR) protocols, all of which are interoperable with their single-user base formulations. The ZNR protocol-extensions are compared with the earlier Takaragi et al multi-user sign-encryption, which is extended from a base-protocol with two random key-pairs following the usual specification of one each of signing and encryption. Both single and double-pair formulations are analysed from the viewpoint of EC equivalence (EQ) establishment, which is required for rigorous multi-sender functionality. We outline a rectification to the original Takaragi et al formulation; thereby enabling parameter-share verification, but at significantly increased overheads. This enables comprehensive equivalent-functionality comparisons with the various multi-user ZNR protocol-extensions. The single-pair ZNR approach is shown to be significantly more efficient, in some cases demonstrating a two/three-fold advantage.
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