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There are many examples in cryptography. Much of progress in cryptography is driven by academic research. …

They're not weak for use with RSA. You don't cite where you got that misconception from, so it's hard for me to respond or identify the source of your confusion -- but you have a faulty premise. Giv …

One approach is to use what is known as format-preserving encryption. For instance, you could use VIL mode or FFX mode. I recommend you spend some quality time on Cryptography.SE and with some resea …

See https://en.wikipedia.org/wiki/Secure_multi-party_computation and a good textbook on theoretical cryptography. …

No cryptography is needed. You just need a way to randomly pick one student in the room, in a fair way. This could be done with numbered balls in a box, or any number of other ways. …

As @mhum suggests, looking at techniques from the field of steganography is probably an excellent starting point... but you might also be interested in subliminal channels.

This is known as the fair exchange problem. There's lots of research on the topic; see the link for an overview and starting point.

Cryptography probably isn't especially useful for enabling Alice to tell whether the user got the right file, but it is useful for enabling the user to tell whether they got the right file. … I don't know of any way that cryptography can allow the user to prove he didn't get the right thing from Bob. As a simple case, suppose the user claims he received nothing from Bob. …

In certain very specific situations, you might be able to use software-based attestation. See, e.g., the following seminal paper: Pioneer: Verifying Code Integrity and Enforcing Untampered Code Exe …

In some sense, it's not surprising that FHE is a lot slower than traditional cryptography. FHE imposes some very strong requirements on the encryption scheme. … Algorithms for black box fields and their application to cryptography. Dan Boneh, Richard Lipton. CRYPTO '96. …

It sounds like your issue is just understanding the notation. Commas indicate concatenation. $\odot$ denotes the dot product. So, $f(x)$ is $|x|$ bits long, $r$ is $|x|$ bits long, and $x \odot r$ is …

There's a problem with the formal details of your definition of collision-resistance: if we take it seriously, then no function (whose output is shorter than its input) can ever be collision-resistant …

The first stage of the BB84 protocol involves throwing away any measurements where the measurements were performed with a different basis. After throwing those away, we are left with the following bi …

I think you actually want secure multi-party computation, not zero-knowledge proofs. In secure multi-party computation, Alice has a secret input $a$, Bob has a secret input $b$, and we want to comput …

There is no strong technical reason. We could have used Diffie-Hellman (with appropriate signatures) just as well as RSA. So why RSA? As far as I can tell, non-technical historical reasons dominate …