Odd-Char Multivariate Hidden Field Equations.
Chia-Hsin Owen Chen, Ming-Syan Chen⋆, Jíntai Ding, Fabian Werner, Bo‐Yin Yang · 2008
We present a multivariate version of Hidden Field Equations (HFE) over a finite eld of odd characteristic, with an extra embedding modifier. Combining these known ideas makes our new MPKC (multivariate public key cryptosystem) more efficient and scalable than any other extant multivariate encryption scheme. Switching to odd characteristics in HFE-like schemes affects how an attacker can make use of field equations. Extensive empirical tests (using magma-2.14, the best commercially available F4 implementation) suggests that our new construction is indeed secure against algebraic attacks using Gröbner Basis algorithms. The embedding serves both to narrow down choices of pre-images and to guard against a possible Kipnis-Shamir type (rank) attack. We may hence reasonably argue that for practical sizes, prior attacks take exponential time. We demonstrate that our construction is in fact efficient by implementing practical-sized examples of our odd-char HFE with 3 variables ( THFE) over F31. To be precise, our preliminary THFE implementation is 15 × 20 × the speed of RSA-1024.