xmeehan

Not OP, but the main threat to cryptography from quantum computing as I understand it is the ability to factor very large numbers. RSA, one of the most common public-key cryptography algorithms, is based on the idea that it's easy to multiply two large numbers together but much more difficult to take a number that's the product of two large numbers and return what those two large numbers are. Factoring allows you to determine the private RSA key from the public RSA key. (In general, it's done in reverse: you pick two large numbers and use them to compute your public and private keys, then discard the numbers.) A quantum computer has some special tricks that lets it compute the period of the function f(x)=a^x mod N for an arbitrary a and where N is the large number you want to factor. The period of that function can then be used to compute the factors of N thanks to some group theory magic and Euler's totient function.

I'm a first-year computer science PhD student and my main research interest is cryptography. Also, my background is primarily in physics so my "other" main research interest is in quantum computing. Unfortunately, at my university there aren't any faculty members that share that same intersectionality of interests. Do you have any advice/suggestions/helpful hints for finding a good research direction? (Also, if you know of any fellowships or grants I should look into that would be much appreciated information!)

Thanks in advance!