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By Bernadete Ribeiro, Rudolf F. Albrecht, Andrej Dobnikar, David W. Pearson, Nigel C. Steele

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Ring signatures [7] allow each user from an “ad-hoc” group, the ring, to sign a message such that the signer’s identity remains secret, yet everyone can verify that the message has been signed by someone in the ring. In this sense, anonymous signatures are an attenuation of ring signatures, because for anonymous schemes the signer’s identity only remains undisclosed as long as the parts of the message are unknown. g. [7,4]) or are rather feasibility constructions as in [1]. One advantage of anonymous signatures over ring signature schemes is that anonymity is not bound to a certain group.

Such that m∗ has never been signed by the signing oracle before). 40 M. Fischlin For transforming the attacker A into one for the underlying signature scheme we let ASig(sk,·) (pk) run a black-box simulation of A for input pk = (pk, K, E) where keys K and E are generated by A by running HKGen(1n ) and EKGen(K). Then, A simulates the signing oracle Sig for A as follows: Each time A submits a message m ∈ {0, 1}i(n) to its (putative) signing oracle attacker A first picks r ← {0, 1}t(n) and u ← {0, 1}d(n) and forwards H(K, m; r) to its oracle Sig to get a signature σ.

A signature scheme S = (SKGen, Sig, SVf) consists of efficient algorithms such that SKGen on input 1n generates a key pair (sk, pk) ← SKGen(1n ), algorithm Sig for input sk and a message m ∈ {0, 1}∗ outputs a signature σ ← Sig(sk, m), and algorithm SVf for input pk, m and σ returns a decision bit d ← SVf(pk, m, σ). Furthermore, for all security parameters n ∈ N, all keys (sk, pk) ← SKGen(1n ), all messages m ∈ {0, 1}∗ and all signatures σ ← Sig(sk, m) it holds SVf(pk, m, σ) = 1. A signature scheme S is existentially unforgeable under adaptively chosenmessage attacks (or, for short, unforgeable) if for any efficient algorithm A the probability for (sk, pk) ← SKGen(1n ) and (m∗ , σ ∗ ) ← ASig(sk,·) (pk) such that SVf(pk, m∗ , σ ∗ ) = 1 and m∗ is not among the queries to oracle Sig(sk, ·), is negligible (as a function of n).

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