  Currently there is an active Post-Quantum Cryptography (PQC) solutions
search, which attempts to find cryptographic protocols resistant to attacks by
means of for instance Shor polynomial time algorithm for numerical field
problems like integer factorization (IFP) or the discrete logarithm (DLP). The
use of non-commutative or non-associative structures are, among others, valid
choices for these kinds of protocols. In our case, we focus on a permutation
subgroup of high order and belonging to the symmetric group S381. Using
adequate one-way functions (OWF), we derived a Diffie-Hellman key exchange and
an ElGamal ciphering procedure that only relies on combinatorial operations.
Both OWF pose hard search problems which are assumed as not belonging to BQP
time-complexity class. Obvious advantages of present protocols are their
conceptual simplicity, fast throughput implementations, high cryptanalytic
security and no need for arithmetic operations and therefore extended precision
libraries. Such features make them suitable for low performance and low power
consumption platforms like smart cards, USB-keys and cellphones.
