In the near future, general quantum computers could become a reality.Because of this we have a need for updating our public key infrastructure to resist quantum attacks.Among the many proposed cryptosystems that we could use to replace our modern cryptosystems are the four cryptosystems we will be analysing: McEliece, Classic McEliece, McNie, and NTRUEncrypt.We will cover the cryptosystems in full detail before analysing how secure and how efficient the cryptosystems are.
In the near future, general quantum computers could become a reality.Because of this we have a need for updating our public key infrastructure to resist quantum attacks.Among the many proposed cryptosystems that we could use to replace our modern cryptosystems are the four cryptosystems we will be analysing: McEliece, Classic McEliece, McNie, and NTRUEncrypt.We will cover the cryptosystems in full detail before analysing how secure and how efficient the cryptosystems are.
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum computing indicate that many of the public key cryptosystems currently in use could easily be broken if large-scale quantum computers become technologically feasible. Further, encrypted messages captured and stored in the past could also be decrypted by a future quantum attacker. Since large-scale quantum computers may one day be developed, We need to prepare for that eventuality by analysing modern cryptosystems with respect to attacks with a quantum computer. In this thesis, submitted in fulfilment of the requirements for the degree of Master of Mathematics in Combinatorics & Optimisation at the University of Waterloo, we examine the quantum strengths and vulnerabilities of several of the most popular classical public key cryptosystems.
Public key cryptography, as deployed on the internet today, stands on shaky \nground. For over twenty years now it has been known that the systems in \nwidespread use are insecure against adversaries equipped with quantum computers \n-- a fact that has largely been discounted due to the enormous challenge of \nbuilding such devices. However, research into the development of quantum \ncomputers is accelerating and is producing an abundance of positive results \nthat indicate quantum computers could be built in the near future. As a \nresult, individuals, corporations and government entities are calling for the deployment of \nnew cryptography to replace systems that are vulnerable to quantum \ncryptanalysis. Few satisfying schemes are to be found. \n \nThis work examines the design, parameter selection, and cryptanalysis of a \npost-quantum public key encryption scheme, NTRUEncrypt, and a related \nsignature scheme, NTRUMLS. It is hoped that this analysis will prove useful in \ncomparing these schemes against other candidates that have been proposed to \nreplace existing infrastructure.
The emergence of quantum computing is a serious threat to the principles of modern crypto-logical mathematics. The classical public-key cryptography, including Rivest-Shamir-Adleman (RSA), Elliptic Curve Cryptography (ECC), and Diffie-Hellman are very safe against classical adversaries yet become susceptible to quantum algorithms, including the Shor algorithm, which can easily solve the underlying mathematical problems. This weakness is jeopardizing confidentiality and integrity of the world-wide systems of communication, money transactions, and essential structures, and requires the immediate creation of safe alternatives. The current literature on post-quantum cryptography (PQC) has covered various classes of algorithm, such as lattice-based, code-based, multivariate schemes, and isogeny-based schemes. Although lattice-based approaches like Nth Degree Truncated Polynomial Ring Unit (NTRU) and FrodoKEM can be highly theoretically resistant, they can be computationally and memory-intensive. Cryptosystems based on code such as Classic McEliece are secure but not practicable because they have huge public key sizes. Multivariate schemes like Rainbow, and isogeny-based schemes like Super singular Isogeny Key Encapsulation (SIKE) have been attacked recently by cryptanalytic attacks, and broken completely. Such restrictions open the necessity to find more efficient and secure quantum-resistant solutions.This research study postulates a hybrid post-quantum cryptographic (PQC) system that combines CRYSTALS-Kyber for encryption with CRYSTALS-Dilithium for digital signatures both of which are approved through the National Institute of Standards and Technology (NIST) PQC standardization program. The model will be such that it ensures quantum resistance but at the same time it will be scalable, efficient and compatible with the existing infrastructures. The test outcomes indicate that the hybrid PQC model is 35-45 percent faster to encrypt and decrypt, signature performance is enhanced by up to 40 percent, and the throughput is 20 times higher (98.7 Mbps) than the same base PQC scheme including Nth Degree Truncated Polynomial Ring Unit (NTRU), McEliece and Rainbow. These enhancements affirm that the suggested model provides a viable trade-off between the security, speed, and efficiency in terms of key size, which makes it a viable and a sound base to ensure secure communication in the quantum age.
The standard public-key cryptosystems used today relies mathematical problems that require a lot of computing force to solve, so much that, with the right parameters, they are computationally unsolvable. But there are quantum algorithms that are able to solve these problems in much shorter time. These quantum algorithms have been known for many years, but have only been a problem in theory because of the lack of quantum computers. But with recent development in the building of quantum computers, the cryptographic world is looking for quantum-resistant replacements for today’s standard public-key cryptosystems. Public-key cryptosystems based on lattices are possible replacements. This thesis presents several possible candidates for new standard public-key cryptosystems, mainly NTRU and ring-LWE-based systems. The latticebased cryptosystems are shown to be very fast and have strong, provable security against quantum computers, but are a lot more complicated than RSA and Diffie-Hellman.
As quantum computing advances, traditional cryptographic schemes such as RSA face increasing vulnerability to attacks. This investigative study delves into the realm of post-quantum cryptography, focusing specifically on variants of RSA designed to resist quantum attacks. Through a comprehensive review of existing literature and cryptographic protocols, we analyse the strengths and weaknesses of various post-quantum RSA variants, including lattice-based, code-based, and hash-based approaches. Additionally, we evaluate the computational efficiency and security guarantees of these variants, considering factors such as key size, encryption/decryption speed, and resistance to quantum algorithms. Our findings provide insights into the current state of post-quantum RSA, highlighting promising directions for further research and development in the quest for quantum-resistant cryptographic solutions. In the future robust variants of RSA, algorithms will help the stakeholders of the cryptosystems to instil faith in the security of the system in the face of challenges which is inadvertently posed by the attackers using advanced security attack vectors.