Multivariate cryptographic schemes that perform digital signatures like HFEv, FLASH and Quartz have something in common. As opposed to enciphering data like in a normal cryptosystem where a public multivariate polynomial $P(X)$ is given as:
$$P(X) = P(p_1(x_1,\ldots,x_n),\ldots,p_n(x_1,\ldots,x_n))$$
You input the plaintext bits $x=(x_1,\ldots,x_n)$ into $...
scrypt is actually a password-based key derivation function (PBKDF *) created by Colin Percival; Stronger Key Derivation via Sequential Memory-Hard Functions. We want slower PBKDF functions since it will slow the attack times. The below is from hashcat performance;
scrpyt 1172.8 kH/s (16.61ms)
With Elliptic Curves, we can compute the order of any point (and, in particular, the point $nP$; this is especially easy on the curves we actually use for ECC, because those curves typically have an order $hq$, for a small $h$ and a large prime $q$ (and the order of any point is a divisor of $hq$).
So, if $q$ is the order of the point $nP$, and if $n$ is ...
There is the idea of a fuzzy vault, a coding theory based idea first proposed by Juels,
developed for biometric applications, it warrants a look.
Start at Wikipedia. These notes below are excellent:
Actually, lecturers/professors build simplified version of block ciphers and hash functions so that the students can understand better.
For Block ciphers there are;
Simplified DES by Edward Schaefer in 96. You can also set it in Stinson's book Appendix G.
Simplified AES is first appeared on Cryptologia, 2003 by Musa, Schaefer, and Wedig.