I went to a talk at Stanford by Eran Tromer on Wednesday, in which he described some of the theory behind Zcash. He made a lot of very strong claims about his new approach to computer security. There was a lot of hand-waving. I don't understand exactly what he's claiming, and what he claims to have proved. You can watch the video yourself and try to figure it out.[1]
Tromer's paper [2] may be helpful. At least there, the references are cited and findable. Tromer's first result deals with collision-resistant hash functions. That's been a big headache in practice.
It's really hard to develop a cryptographic hash function for which someone can't create two strings that result in the same hash.[3] MD4 and MD5 have been broken, SHA-1 has been partially broken, and SHA-256 hasn't been (publicly) broken yet. Tromer seems to claiming that he has a solution to weak hash functions. But it's really hard to tell from his writing.
Anybody really understand this?
[1] http://web.stanford.edu/class/ee380/
[2] http://www.cs.tau.ac.il/~tromer/papers/huntingsnark-20140724...
[3] https://www.cs.cornell.edu/courses/cs6830/2009fa/scribes/lec...