Key Substitution Attacks on Lattice Signature Schemes Based on SIS Problem

Table 1

Key substitution attacks (KSA) on signature schemes based on SIS problem.

Scheme	Target equation for KSA	Result
GPV [7]		insecure
Lyubashevsky [8]		insecure
matrix-BLISS [9]		insecure
ring-BLISS [9]
-GPV		unknown
-Lyubashevsky		secure
-matrix-BLISS		secure
-ring-BLISS		secure

Insecure under some conditions.