cryptosystem
cryptography
multivariate quadratic (MQ) problem
solving strategies
solution
Short Solutions to Nonlinear Systems of Equations
requirements
equations
hard problem
71-90
joint requirements
possibility
function
new hard problem
strategies
chapter
secure hash function
algorithm
lattice reduction
false
representation
2022-11-24T21:15
key cryptosystem
2018-02-28
public key cryptosystem
https://doi.org/10.1007/978-3-319-76620-1_5
system of equations
This paper presents a new hard problem for use in cryptography, called Short Solutions to Nonlinear Equations (SSNE). This problem generalizes the Multivariate Quadratic (MQ) problem by requiring the solution be short; as well as the Short Integer Solutions (SIS) problem by requiring the underlying system of equations be nonlinear. The joint requirement causes common solving strategies such as lattice reduction or Gröbner basis algorithms to fail, and as a result SSNE admits shorter representations of equally hard problems. We show that SSNE can be used as the basis for a provably secure hash function. Despite failing to find public key cryptosystems relying on SSNE, we remain hopeful about that possibility.
hash function
basis
2018-02-28
system
nonlinear systems
quadratic problem
basis algorithm
problem
short solution
use
paper
reduction
short integer solution problem
short representations
solution problem
chapters
nonlinear equations
https://scigraph.springernature.com/explorer/license/
Gröbner basis algorithm
pub.1101242709
dimensions_id
Mathematical Sciences
imec-COSIC, KU Leuven, Leuven, Belgium
imec-COSIC, KU Leuven, Leuven, Belgium
Pure Mathematics
Pomykała
Jacek
Szepieniec
Alan
Bart
Preneel
Springer Nature - SN SciGraph project
978-3-319-76620-1
978-3-319-76619-5
Number-Theoretic Methods in Cryptology
Pieprzyk
Josef
Jerzy
Kaczorowski
doi
10.1007/978-3-319-76620-1_5
Springer Nature