Concurrent Blind Signatures Without Random Oracles

We present a blind signature scheme that is efficient and provably secure without random oracles under concurrent attacks utilizing only four moves of short communication. The scheme is based on elliptic curve groups for which a bilinear map exists and on extractable and equivocal commitments. The unforgeability of the employed signature scheme is guaranteed by the LRSW assumption while the blindness property of our scheme is guaranteed by the Decisional Linear Diffie-Hellman assumption. We prove our construction secure under the above assumptions as well as Paillier's DCR assumption in the concurrent attack model of Juels, Luby and Ostrovsky from Crypto '97 using a common reference string. Our construction is the first efficient construction for blind signatures in such a concurrent model without random oracles. We present two variants of our basic protocol: first, a blind signature scheme where blindness still holds even if the public-key generation is maliciously controlled; second, a blind signature scheme that incorporates a “public-tagging” mechanism. This latter variant of our scheme gives rise to a partially blind signature with essentially the same efficiency and security properties as our basic scheme.