Tropical Cryptography Based on Multiple Exponentiation Problem of Matrices

Table 1

Comparison among relevant tropical schemes.

Schemes	Mathematical problems	KU attack	RM attack	G-KU attack
Grigoriev [16]	Two-side matrix action problem	×	√	×
Grigoriev [18]	Semi-direct product problem	√	×	√
Muanalifah [22]	Two-side matrix action problem	√	√	×
Our schemes	Multiple exponentiation problem	√	√	√

Note. that √ means that the scheme can resist the corresponding attack, while × does not.