Key Exchange Protocol Based on the Matrix Power Function Defined Over "Equation missing"

Sigma Identification Protocol Construction Based on MPF Defined over Non-Commuting Platform Group

“…This comes from an assumption that NP-complete problems are hard to crack even for quantum computers. Important to note is the fact that we used the same templates defined in [8]. Notably, DLP does not provide sufficient security against quantum cryptanalysis.…”

“…In this paper, we continue our research in the non-commuting asymmetric cryptography field. Recently we demonstrated how two users can agree on a shared key by executing a key exchange protocol based on the MPF defined over a non-commuting platform group [8]. There we used highly non-linear matrix mapping, where the entries of the base matrix were chosen from a non-commuting modular group of size 16.…”

“…This is precisely the idea we used previously to construct a working key exchange between Alice and Bob. Further examination of the properties of MPF defined over M 16 has shown that the templates presented in [8] are suitable for our current goals. Hence, in this paper, we present SIP based on the MPF defined over the non-commuting group M 16 .…”

“…To overcome the absence of these properties in [8], we defined templates for the base matrix W and both power matrices X and Y. We revise these templates in the next section to keep everything in one place.…”

“…Publicly fixed parameters are the modular group M 16 , the ring of integers Z 8 , and the order of the square matrices m. Matrix W ∈ Mat m (M 16 ) is chosen randomly according to the presented template (6) and is published online. Moreover, public matrices L and R, satisfying templates (7) and (8), respectively, are chosen.…”