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Here is how you do a literature search, to find relevant research papers in the literature: You identify some search terms related to your topic, and search for them on Google Scholar and other places (e.g., Crypto.SE, via web search, on Citeseer). (For cryptographic work, also try searching Google with site:eprint.iacr.org and your search terms, to turn ...

It depends on whether you're in university or not. If you are and your school has the for-pay journals, start by searching them for the topic. Also try 'eprint.iacr.org' and google scholar. To find the most important or seminal papers in a topic you should look at the number of people that have cited it. This is an imperfect but useful heuristic for ...

You can solve this using mixnets. Sample protocol: The parties jointly choose a public/private keypair, such that the random key is shared among all $n$ parties. (This is threshold crypto, and there are standard protocols for this.) Each party $P_i$ encrypts his/her value $v_i$ under the public key chosen in step 1. He/she broadcasts this ciphertext ...

All mathematical groups can be used to perform an ElGamal encryption, so that is a first kind of math. That's where elliptic curves are useful: they have a group structure. If you find a group, you can build a cryptosystem out of it. However, as @poncho pointed out, different groups have different properties with regards to security. For instance, elliptic ...

Not sure what you are trying to do but are you not approaching it the wrong way? NIST already recommends algoorithms/ciphers for use in their environments. This means they have vetted these and are deemed secure. Now you want performance as well. So use openssl and see which of the algorithms are of acceptable performance to you. Like you said choose key ...