IACR News item: 21 August 2012
Jae Hong Seo
ePrint ReportWe propose short signatures from the DH assumption, which has a sublinear size public key. More precisely, our proposal produces a public key of $\\Theta(\\sqrt{\\frac{\\lambda}{\\log \\lambda}})$ group elements. Our construction is inspired from two techniques for short signatures such as using programmable hashes and using tags. From two previous techniques, we first derive a signature scheme with a somewhat short public key of $\\Theta(\\frac{\\lambda}{\\log\\lambda})$, and then we developed a new technique for {\\em asymmetric trade} between the public key size and the signature size. In particular, by adding one field element in each signature, we can reduce the public key size to $O(\\sqrt{\\frac{\\lambda}{\\log \\lambda}})$ group elements, so that the resulting signature size is two group elements and two field elements.
We also propose a variant by applying a technique for compressing tag vectors so that the resulting signatures has a shorter signature size (two group elements and one field element) by augmenting signing/verification costs and adding constant factor in public key size (that is, public key size is still $\\Theta(\\sqrt\\frac{\\lambda}{\\log\\lambda})$ group elements). Note that we limit ourselves to dealing with only polynomial-time reductions in all security proofs.
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