It appears there there were interesting things going on in cryptography: the first homomorphic encryption scheme appeared recently (explanation, HT). Roughly speaking, it is a way of encoding x into f(x) such that you can compute f(x+y) easily knowing f(x) and f(y) even though you can't easily restore x and y (and same for f(x*y)).
What are practical applications for schemes of this type (once their security has been established)? To me, it appears they could make writing algorithms for manipulating private data much easier.
Here are my thoughts:
- electronic voting
- checking the integrity of private data
- is there a chance that would help privacy in general?
Example: I have accounts with Banks A, B, C. Entity X wants to confirm I have more than $1000 total; it would happily accept statements from Banks A, B, C or D, but unfortunately I don't have enough money in any single account. Bank A encrypts the info about my $500 dollars with my public key; similarly, Banks B and C encrypt the info that I have $200 and $300 respectively. They send these data to X who adds them to some number which I demonstrate to be in fact encrypted $1000 (by encrypting $1000 with my public key and demonstrating that the result is the same). I have proved something without disclosing to X how much money I have in each account.
Another example: Good citizens X_1, ... , X_n are teaming up to select one of two candidates, one of which is latte-drinking liberAl while another is a