Implementation of key-exchange based on CLT13 multilinear maps

This is an implementation in Sage of the algorithms described in the paper:

• [CP18] J. S. Coron, H. V. L. Pereira, "On Kilian's Randomization of Multilinear Map Encodings". IACR Cryptology ePrint Archive 2018: 1129 (2018)

Key-exchange based on CLT13 multilinear maps

• Sage implementation

Implementation of the lattice attacks

• Orthogonal lattice attack against the Approximate-GCD problem
• Orthogonal lattice attack against the vector Approximate-GCD problem

Implementation of the GCD attacks

• Chen-Nguyen attack
• Lee-Seo attack
• Our GCD attack against the vector variant

Implementation of the Cheon et al. attacks

• Basic Cheon et al. attack
• Cheon et al. attack with matrices
• Tensoring attack