Post-Quantum Cryptography (PQC) attempts to find cryptographic protocols resistant to attacks by means of for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP). Other aspects are the backdoors discovered in deterministic random generators or recent advances in solving some instances of DLP. The use of alternative algebraic structures like non-commutative or non-associative partial groupoids, magmas, monoids, semigroups, quasigroups or groups, are valid choices for these new kinds of protocols. In this paper, we focus in an asymmetric cipher based on a generalized ElGamal non-arbitrated protocol using a non-commutative general linear group. The developed protocol forces a hard subgroup membership search problem into a non-commutative structure. The protocol involves at first a generalized Diffie-Hellman key interchange and further on the private and public parameters are recursively updated each time a new cipher session is launched. Security is based on a hard variation of the Generalized Symmetric Decomposition Problem (GSDP). Working with GF(2518) a 64-bits security is achieved, and if GF(25116) is chosen, the security rises to 127-bits. An appealing feature is that there is no need for big number libraries as all arithmetic if performed in Z251 and therefore the new protocol is particularly useful for computational platforms with very limited capabilities like smartphones or smartcards.

Providing Privacy and security for aggregated data in wireless sensor networks has drawn the attention of practicing engineers and researchers globally. Several cryptographic methods have been already proposed to solve security and data integrity problems for aggregated data. Matrix cryptography is a better option for creating secure encryption/decryption algorithms to counter quantum attack. However, these algorithms have higher computational cost and increased communication overhead. Hence, a new technique of loss-less secure data aggregation in Clustered Wireless Sensor Networks is presented. The proposed method uses integer matrices as keys for data security and data integrity. Matrix operations are carried out in finite field Zp. Loss-less secure data aggregation is extended for homomorphic summation while the cipher text expansion ratio is kept substantially low. The proposed algorithm has inbuilt fast and efficient signature verification facility. The execution time of our signature verification mechanism is found to be approximately 50 percent less compared to a couple of standard existing signature verification schemes.