Public key encryption methods are often used to create a digital signature, and where Bob has a public key and a private key. In order to prove his identity, he will encrypt something related to the message with his private key, and which can then be checked with his public key. The main current methods of public-key encryption include RSA and ECC (Elliptic Curve Cryptography), and which involve computationally difficult operations. But these operations have not been proven to be hard in an era of quantum computers. One well-known hard problem is the solving of quadratic equations with $m$ equations with $n$ variables. This is a known NP-hard problem, even in a world of quantum computers. These can be used as post-quantum signature schemes and which involve multivariate equations. In order to understand these methods, this paper outlines a simple example of implementing the oil and vinegar method, and where we have a number of unknown oil variables and a number of known vinegar variables, and where the vinegar variables help convert the hard problem into an easy one.

As the embedded device and internet of things (IoTs) concept prevalent in today's world, there is an increasing demand for the security and performance requirements on deploying these devices to private and public sectors. The crucial part of it is to protect privacy, confidentiality and integrity, meanwhile, maintain an adequate level of performance during transmission, storage and access of critical information. While the conventional cryptography methods, such as the Advanced Encryption Standard (AES), SHA$-$2 hashing method and RSA and Diffie Hellman for message authentication and identification, work well on systems which have reasonable processing power and memory capabilities. These do not scale well into a world with embedded systems and sensor networks, in conjunction with their nature of smaller size and lower cost. Thus, in the context of resource constrained device, lightweight cryptography methods are proposed to overcome many of the problems of conventional cryptography possessed. This includes constraints related to physical size, processing requirement, memory limitation, energy drain and production cost. This paper provides a survey of the architectures that are defined as replacements for conventional ciphers within an IoTs space and discuss some trends in the design of future lightweight algorithms. The performance metrics are carefully chosen to reflect and assess the suitability for embedded devices. The aim of this research is to identify the various performance metrics applied on different types of symmetric block ciphers especially lightweight ciphers and compare the results on versatile platforms with stream ciphers and public key methods. The comparative analysis on efficient LW cipher will be tested against other similar block ciphers on both MacBook Pro with Intel core and resource constrained device Raspberry Pi with ARM processor.