Abstract
We introduce a new computational problem related to the interpolation of group homomorphisms which generalizes many famous cryptographic problems including discrete logarithm, Diffie-Hellman, and RSA. As an application, we propose a generic undeniable signaturescheme which generalizes the MOVA schemes. Our scheme is generic in the sense that we transform a private group homomorphism from public groups G to H (the order of H being public) into an undeniable signature scheme. It is provably secure in the random oracle model provided that the interpolation problem is hard and it offers the advantage of making the signature size arbitrarily short (depending on a security level). We (im)prove some security results from MOVA. We also propose a new example with complexity similar to RSA and with 3-byte signatures.
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Monnerat, J., Vaudenay, S. (2004). Generic Homomorphic Undeniable Signatures. In: Lee, P.J. (eds) Advances in Cryptology - ASIACRYPT 2004. ASIACRYPT 2004. Lecture Notes in Computer Science, vol 3329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30539-2_25
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