Secret government revisited

Rational Secret Sharing, Revisited

We consider the problem of secret sharing among n rational players. This problem was introduced by Halpern and Teague (STOC 2004), who claim that a solution is impossible for n = 2 but show a solution for the case n ≥ 3. Contrary to their claim, we show a protocol for rational secret sharing among n = 2 players; our protocol extends to the case n ≥ 3, where it is simpler than the Halpern-Teague...

Computational Verifiable Secret Sharing Revisited

Verifiable secret sharing (VSS) is an important primitive in distributed cryptography that allows a dealer to share a secret among n parties in the presence of an adversary controlling at most t of them. In the computational setting, the feasibility of VSS schemes based on commitments was established over two decades ago. Interestingly, all known computational VSS schemes rely on the homomorphi...

Low Secret Exponent RSA Revisited

We present a lattice attack on low exponent RSA with short secret exponent d = N for every δ < 0.29. The attack is a variation of an approach by Boneh and Durfee [4] based on lattice reduction techniques and Coppersmith’s method for finding small roots of modular polynomial equations. Although our results are slightly worse than the results of Boneh and Durfee they have several interesting feat...

The Growth of Government Revisited

Threshold changeable secret sharing schemes revisited

This paper studies the methods for changing thresholds in the absence of secure channels after the setup of threshold secret sharing schemes. First, we construct a perfect (t, n) threshold scheme that is threshold changeable to t ′ > t , which is optimal with respect to the share size. This improves the scheme of Wang and Wong by relaxing the requirement from q ≥ n + v to q > n with the secret-...