The ever expanding horizon of computational abilities of the quantum computers pose a great threat to modern day cryptographic algorithms and to the field of cryptography as a whole. The threat that quantum computation will eventually reach a point at which it will be capable of solving hard problems within minutes which would take years for classical computers to even scratch the surface. But the world of cryptography, can be saved from this inevitable collapse. This can be done by the using Post-Quantum Cryptography, which as the name suggests, is the aggregation of the methods and techniques that are resistant to even the mighty computing power of the quantum computers, and thus can be used to keep cryptography alive even in the post-quantum era. This paper proposes a similar kind of algorithm, namely Qu.En.Al.(Quintic Encryption Algorithm), one that is based of the mathematical foundations of Abstract Algebra, specifically the Abel-Ruffini theorem [7]. The QuEnAl algorithm uses an asymmetric key encryption methodology to create a safe and secure cryptosystem that can be used to exchange data between users in a protected manner. Just like others among the group, QuEnAl uphold security and privacy even in against quantum brute-force attacks as the problem it is based upon is not only hard to solve, it is mathematically proven to be impossible to deduce. This gives it an edge over the other post-quantum algorithms. This algorithm can be applied over a plethora of different areas like Encryption/Decryption Crypto-systems, Online Security, Net-Banking etc. where information being transmitted is confidential and demands privacy.