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... Computational Diffie-Hellman problem in gap groups) and to the so-called Strong Diffie-Hellman assumption, respectively. It is worth noticing that even after subsequent performance improvements (see =-=[3]-=-), pairing-based cryptosystems are less efficient than the schemes we shall describe later. Unfortunately, there are still no practical digital signature schemes that have been proven secure by a stan...

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...rong RSA assumption (SRSA). (The SRSA states that given z in Z∗ n , the multiplicative residues modulo n, it is hard to find an integer e > 1 and t ∈ Z∗ n such that te = 1 mod n. It was introduced in =-=[2]-=-.) Gap Diffie-Hellman (GDH) groups provide another setting where provably secure signatures in the standard model have been constructed. A GDH group is any group where the Computational Diffie-Hellman...

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...gnature paradigm, and in particular we show a reduction (in the standard model) from our scheme to a twin signature construction in section §5. The modified Nyberg-Rueppel signature (mNR, proposed in =-=[1]-=-) has provable security in the generic model; the proof we include herein is inspired by techniques in [32]. The signature produces a triplet of signing values (including the message itself) – as oppo...