Torsion Limits and Riemann-Roch Systems for Function Fields and Applications, by Ignacio Cascudo and Ronald Cramer and Chaoping Xing
The Ihara limit (or constant) $A(q)$ has been a central problem of study in the asymptotic theory of global function fields (or equivalently, algebraic curves over finite fields). It addresses global function fields with many rational points and,
so far, most applications of this theory do not
require additional properties. Motivated by recent applications, we require global function fields
with the additional property that their zero class divisor groups contain at most a small number of $d$-torsion points. We capture this with the notion of torsion limit, a new asymptotic quantity for global function fields.
It seems that it is even harder to determine values of this new quantity than the Ihara constant.
Nevertheless, some non-trivial upper bounds are derived.
Apart from this new asymptotic quantity and bounds on it, we also introduce Riemann-Roch systems of equations. It turns out that this type of equation system
plays an important role in the study of several other problems in each of these areas: arithmetic secret sharing, symmetric bilinear complexity of multiplication in finite fields, frameproof codes and the theory of error correcting codes.
Finally, we show how our new asymptotic quantity, our bounds on it and Riemann-Roch systems can be used to improve results in these areas.
The M3lcrypt Password Based Key Derivation Function, by Isaiah Makwakwa
M3lcrypt (canonical M3lcryptH) is a password based key derivation
function built around the Merkle-Damgard hash function H. It supports
large [pseudo]random salt values ( 128-bit) and password lengths.
ZAPs and Non-Interactive Witness Indistinguishability from Indistinguishability Obfuscation, by Nir Bitansky and Omer Paneth
We present new constructions of two-message and one-message witness-indistinguishable proofs (ZAPs and NIWIs). This includes:
ZAP (or, equivalently, non-interactive zero-knowledge in the common random string model) from indistinguishability obfuscation and one-way functions.
NIWIs from indistinguishability obfuscation and one-way permutations.
The previous construction of ZAPs [Dwork and Naor, FOCS 00] was based on trapdoor permutations. The two previous NIWI constructions were based either on ZAPs and a derandomization-type complexity assumption [Barak, Ong, and Vadhan CRYPTO 03], or on a specific number theoretic assumption in bilinear groups [Groth, Sahai, and Ostrovsky, CRYPTO 06].