Application of hourglass matrix in Goldreich-Goldwasser-Halevi encryption scheme

Abstract

Goldreich-Goldwasser-Halevi (GGH) encryption scheme is lattice-based cryptography with its security based on the shortest vector problem (SVP) and closest vector problem (CVP) with immunity to almost all attacks, including Shor's quantum algorithm and Nguyen's attack of higher lattice dimension. To improve the efficiency and security of the GGH Scheme by reducing the size of the public basis to be transmitted, we use an hourglass matrix obtained from quadrant interlocking factorization as a public key. The technique of quadrant interlocking factorization to yield a nonsingular hourglass matrix compensates the encryption scheme with better efficiency and security.

A Review on Quadrant Interlocking Factorization: WZ and WH Factorization

“…W H factorization has great tendency in usage than W Z factorization. First, though with little evidence it has been proposed that the linearly independent columns of hourglass matrix forming the basis vectors of a lattice will make it suitable for lattice-base cryptography, especially in GGH -Goldreich-Goldwasser-Halevi encryption scheme, see [47,46]. The usage of hourglass matrix is expected to be able to reduce the size of bases.…”