The technology encompasses new uses of already-known cryptographic techniques. The technology entails computer-based methods of sharing information securely, in particular an asymmetric method of secure computation that relies on the private-key/public key paradigm with homomorphic encryption. The methods and programmed computing apparatuses herein harness mathematical concepts and apply them to services or tasks that are commercially useful and that have not hitherto been possible. Applications of the methods and apparatus herein are far-ranging and include, but are not limited to: purchase-sale transactions such as real estate or automobiles, where some aspect of price negotiation is expected; stock markets; legal settlements; salary negotiation; auctions, and other types of complex financial transactions.