Amos Beimel, Yehuda Lindell, Eran Omri, and Ilan Orlov
Ben Gurion University; Bar Ilan University; Bar Ilan University; and Ben Gurion University
Abstract. A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation, where parties give their inputs to a trusted party which returns the output of the functionality to all parties. In particular, in the ideal model such computation is fair -- all parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition—1/p-secure computation—which guarantees partial fairness. For two parties, they construct 1/p-secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols.
We study 1/p-secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/p-secure protocols that are resilient against any number of corrupt parties provided that the number of parties is constant and the size of the range of the functionality is at most polynomial (in the security parameter n). If less than 2/3 of the parties are corrupt, the size of the domain is constant, and the functionality is deterministic, then our protocols are efficient even when the number of parties is log log n. On the negative side, we show that when the number of parties is super-constant, 1/p-secure protocols are not possible when the size of the domain is polynomial. Thus, our feasibility results for 1/p-secure computation are essentially tight.
We further motivate our results by constructing protocols with stronger guarantees: If in the execution of the protocol there is a majority of honest parties, then our protocols provide full security. However, if only a minority of the parties are honest, then our protocols are 1/p-secure. Thus, our protocols provide the best of both worlds, where the 1/p-security is only a fall-back option if there is no honest majority.
After partnering with Wirex, the company was able to add XRP token support to its Visa card. Subsequently, the number of sign-ups and transactions on the platform had a considerable boost.
The very fine qualities of XRP continue to pull users and firms towards itself with the latest addition of Bitcoin Superstore. Earlier this year, Brad Garlinghouse, the CEO of Ripple said the only way of XRP decoupling from Bitcoin influence is through mass adoption.
This movement has supported the saying that the token has more utility than predicted and in fact the firm pushed up ahead and donated millions for humanitarian causes and charity. The first feedback was not that big, however judging from the most recent development Ripple is enjoying the last piece of the cake.
With the above announcement by Bitcoin Superstore via their twitter handle, users can almost in an instant complete settlements with XRP while purchasing from different retail outlets. These outlets being the leading ones like eBay, Amazon and others. If you choose to go for this option remember that XRP in the past has given out results of being cheap for both the merchant offering to accept the token and the user.
Or, even shorter, build a massive, level playing field in which assets can compete to bridge payments, then try to make XRP a winner on that playing field.
This is an ambitious, maybe even crazy, plan. But Ripple has raised tens of millions of dollars, has over a hundred full time employees, and our successes to date speak for themselves. That is, of course, no guarantee of success.