Statement of the ProblemThe world has become one globalized platform with the advent of sophisticated embedded systems as it allows people to communicate in the local town to the farthest town on this earth.This includes communicating via mobile phones, Internet or sending an instruction to microwave oven, television and other wireless systems.We make assumptions that our communication remains confidential when we communicate using mobile phones or Internet.We assume that the payment gateway will be authenticated and our banking details will remain confidential, while accessing Internet banking.We assume that our instruction sent to the wireless embedded systems will be received exactly as we had sent (Integrity) i.e. the message sent by us and the message received by the embedded system will be the same.We make these assumptions as there will be certain protocols followed to maintain security standards.The security of these protocols is generally based on certain computationally 'hard' problems such as factoring a very large number.These are computationally hard problems to solve due to limited computational resources.If a quantum computer will be built, then these problems will no longer remain computationally hard.They will be solved in polynomial time complexity.Hence, our messages will remain neither confidential nor have integrity.Network communication will, no longer be able to authenticate.Similarly, electronic travel documents will not remain secured.Today, travel documents are an integral part of the daily routine.Among these travel documents, passports allow the holder's identity to be verified.This protects the nations against illegitimate immigrants, criminals and terrorists.Similar to the above mentioned scenario, advent of quantum computers will allow forfeiting of passports.It will also allow access to personal information.Hence, posing risk to millions of lives. Methods and ProceduresTo conquer these issues, we propose to conduct research on replacing the current travel document protocols by using Lattice-based cryptography.This could be replicated in all other network based embedded systems.We are motivated to use Latticebased cryptography as it is one of the important classes of the post-quantum cryptography algorithms.Lattice based algorithms are important due to significant research by scientific community, well-known underlying lattice problems and computational efficiency.
Statement of the ProblemThe world has become one globalized platform with the advent of sophisticated embedded systems as it allows people to communicate in the local town to the farthest town on this earth.This includes communicating via mobile phones, Internet or sending an instruction to microwave oven, television and other wireless systems.We make assumptions that our communication remains confidential when we communicate using mobile phones or Internet.We assume that the payment gateway will be authenticated and our banking details will remain confidential, while accessing Internet banking.We assume that our instruction sent to the wireless embedded systems will be received exactly as we had sent (Integrity) i.e. the message sent by us and the message received by the embedded system will be the same.We make these assumptions as there will be certain protocols followed to maintain security standards.The security of these protocols is generally based on certain computationally 'hard' problems such as factoring a very large number.These are computationally hard problems to solve due to limited computational resources.If a quantum computer will be built, then these problems will no longer remain computationally hard.They will be solved in polynomial time complexity.Hence, our messages will remain neither confidential nor have integrity.Network communication will, no longer be able to authenticate.Similarly, electronic travel documents will not remain secured.Today, travel documents are an integral part of the daily routine.Among these travel documents, passports allow the holder's identity to be verified.This protects the nations against illegitimate immigrants, criminals and terrorists.Similar to the above mentioned scenario, advent of quantum computers will allow forfeiting of passports.It will also allow access to personal information.Hence, posing risk to millions of lives. Methods and ProceduresTo conquer these issues, we propose to conduct research on replacing the current travel document protocols by using Lattice-based cryptography.This could be replicated in all other network based embedded systems.We are motivated to use Latticebased cryptography as it is one of the important classes of the post-quantum cryptography algorithms.Lattice based algorithms are important due to significant research by scientific community, well-known underlying lattice problems and computational efficiency.
Classical cryptography has been around for a long time in the documented human history, but most classical ciphers were broken and even solved by hand. Shannon introduced the notion of perfect secrecy that formally defines confidentiality in the information-theoretic sense, which is only possible in the restricted scenarios where the message is no longer than the encryption key. The invention of public-key cryptography (the Diffie-Hellman key exchange protocol in 1976 and the RSA crypto-system in 1977) marks the birth of modern cryptography, allowing parties to exchange messages securely without sharing any secrets in advance. Furthermore, it provides computational security based on the conjectured hardness of mathematical problems such as factorization and the discrete logarithm. Public-key cryptography has found numerous applications in the Internet, financial and banking industry, and blockchains, and it plays a crucial role in protecting information security and asset safety. Unfortunately, in the 1990s, Shor proposed efficient quantum algorithms that solve number-theoretic problems, including factorization and discrete logarithms in polynomial time. Once a quantum computer of a particular scale becomes a reality, it will cause a devastating blow to the existing public-key infrastructure. To deal with such a ‘quantum crisis’, academia and industry are looking into the design, analysis and standardization of cryptographic algorithms that can resist quantum computers referred to as post-quantum cryptography (PQC). The National Institute of Standards and Technology (NIST) has been soliciting proposals for the post-quantum public-key algorithms since 2016. More recently, the Chinese Association for Cryptologic Research (CACR) held a competition on designing cryptographic algorithms whose public-key cryptography track focused on post-quantum cryptographic algorithms. Lattice-based cryptography is considered by most to be the mainstream technical route of post-quantum cryptography, which is reflected in the number of proposals (and their percentage of the total) received in the NIST PQC process. To reflect the status quo of post-quantum cryptography, we invite leading experts in this area to contribute three technical perspectives that aim to help readers understand the algorithms, the underlying basic techniques and different technical routes to achieve quantum resistance. The first perspective, presented by Lu and Zhang, introduces public-key cryptographic algorithms whose quantum security is reducible from the conjectured quantum hardness of lattice problems. In particular, they mainly focus on public-key encryption (PKE) and the key encapsulation mechanism (KEM), which are essential building blocks for securing the confidentiality of communication without pre-shared secrets. Both types of crypto-systems are solicited by the NIST PQC standardization and the CACR algorithm design competition. This perspective gives a comprehensive survey on practical lattice-based PKEs/KEMs, and their best-known quantum and classical attacks. Another important post-quantum crypto-system is digital signature, which ensures that three goals of information security are met other than confidentiality, namely, integrity, authentication and non-repudiation. The second perspective is on lattice-based signature by Lyubashevsky. In this perspective, he surveys different techniques in building lattice-based post-quantum crypto-systems, discusses the challenges in overcoming performance issues and gives us state-of-the-art digital signature schemes. In addition to ensuring the ‘static’ security of information in storage and transmission, advanced cryptographic algorithms and protocols can guarantee information security during the computation process (possibly among multiple parties), referred to as privacy-preserving computation. Cryptographic techniques involved in privacy-preserving computation include secure multi-party computation, zero-knowledge proof and fully homomorphic encryption. There is a pressing need to migrate them to the post-quantum era. The third perspective, by Yu and Xie, presents practical instantiations of these algorithms and discusses possible ways to migrate them to their quantum-resistant counterparts. To summarize, post-quantum cryptography has received widespread attention and made significant progress in recent years. Some post-quantum cryptographic algorithms, such as the lattice-based candidate, also have other advantages (e.g., computational efficiency and full homomorphism) over their classical counterparts. Lattice-based cryptography is an emerging field with high theoretical value and wide application, and we encourage young researchers to enter and explore this new and exciting field.
Alongside the growth of technology is the increasing demand for security of data and communication channels. As attacking power grows, devices become smaller and data expands, the security needs to be stronger yet less resource-consuming than ever before. Public key cryptography (PKC) is used in the majority of today's communications systems. The security of public-key cryptographic schemes, such as RSA and elliptic curve cryptography (ECC), is based on underlying mathematical problems such as factoring large integers or solving the discrete log problem. However, the discovery of Shor's Algorithm in 1994 insinuates that these schemes will be insecure when a full-scale quantum computer is developed, as these problems will be solvable in polynomial time. Therefore attention has moved towards post-quantum, or quantum-safe, cryptography (QSC). In 2016, the National Institute of Standards and Technology (NIST) announced the beginning of their efforts to migrate to QSC, a standardisation process which has involved the cryptographic community worldwide. There are five main types of QSC being considered for standardisation; lattice-based, code-based, multivariate-based, hash-based and isogeny-based. Lattice-based cryptography (LBC) offers a promising alternative to today's classical approaches. Hard problems based on lattices are believed to be unsolvable, even by a quantum-computer, in a feasible amount of time. In 1995, Ajtai showed that the average case complexity of these problems is at least as hard as solving the problems in the worst case. Furthermore, lattice-based schemes are the only remaining contender in the NIST process to provide the important primitives of encryption, key encapsulation and digital signature schemes (DSSs). A well-recognised open problem surrounding quantum-safe cryptography is its increase in bandwidth and computational complexity in comparison to existing cryptography. However, in comparison to other quantum-safe schemes, LBC has been shown to be relatively efficient. In this thesis, novel software designs of lattice-based schemes are presented and shown to be competitive with existing PKC. Additionally, physical attacks are considered and countermeasures are incorporated into the designs. DSSs are required for authentication, integrity and non-repudiation of data. This thesis provides an evaluation of three leading signature schemes, BLISS-B, Dilithium and \textsc{Falcon}, which vary in terms of their key features, such as the sampling processes used, and the structure of the lattices. Physical attacks on the three schemes are considered and the effect on performance of appropriate attack countermeasures is evaluated. A novel fault attack on the NIST candidate \textsc{Falcon} is also proposed. A further advantage of LBC is the ability to support cryptographic primitives with extended capabilities to facilitate certificate management and compute on encrypted data. The complexity of today's technology advances mean applications require more sophisticated primitives, which contrastingly are required to run on even smaller platforms. This thesis presents novel quantum-safe advanced cryptographic schemes, specifically lattice-based identity-based encryption (IBE) and hierarchical identity-based encryption (HIBE). IBE removes the need for certificate management, as a user's public key depends on their public identity. IBE is currently used in vital applications such as emergency services communication and so the development of a high-performance quantum-safe alternative is imperative. This thesis also introduces the first scalable HIBE scheme based on lattices. The first HIBE scheme based on structured lattices, Latte, was proposed by the National Centre for Cyber Security (NCSC) in 2017. However, the public key and ciphertext sizes increased with each delegation and hence it was not feasible to scale the algorithm. Skinny Latte, proposed in this thesis, remedies this issue by fixing the dimension of the lattice, thereby making public key and ciphertext sizes constant. This research also shows that it is practical for real-world deployment. Overall, this thesis demonstrates that lattice-based cryptography is practical for real-world applications. It considers both theoretical and physical attacks, and presents novel designs of advanced quantum-safe cryptographic primitives, which have only yet been realised by lattices.
Digital signatures are indispensable for security on the Internet, because they guarantee authenticity, integrity, and non-repudiation, of namely e-mails, software updates, and in the Transport Layer Security (TLS) protocol which is used for secure data transfer, for example. Most signature schemes that are currently in use such as the RSA signature scheme, are considered secure as long as the integer factorization problem or the discrete logarithm (DL) problem are computationally hard. At present, no algorithms have yet been found to solve these problems on conventional computers in polynomial time. However, in 1997, Shor published a polynomial-time algorithm that uses quantum computation to solve the integer factorization and the DL problem. In particular, this means that RSA signatures are considered broken as soon as large-scale quantum computers exist. Due to significant advances in the area of quantum computing, it is reasonable to assume that within 20 years, quantum computers that are able to break the RSA scheme, could exist. In order to maintain authenticity, integrity, and non-repudiation of data, cryptographic schemes that cannot be broken by quantum attacks are required. In addition, these so-called post-quantum secure schemes should be sufficiently efficient to be suitable for all established applications. Furthermore, solutions enabling a timely and secure transition from classical to post-quantum schemes are needed. This thesis contributes to the above-mentioned transition. In this thesis, we present the two lattice-based digital signature schemes TESLA and qTESLA, whereby lattice-based cryptography is one of five approaches to construct post-quantum secure schemes. Furthermore, we prove that our signature schemes are secure as long as the so-called Learning With Errors (LWE) problem is computationally hard to solve. It is presumed that even quantum computers cannot solve the LWE problem in polynomial time. The security of our schemes is proven using security reductions. Since our reductions are tight and explicit, efficient instantiations are possible that provably guarantee a selected security level, as long as the corresponding LWE instance provides a certain hardness level. Since both our reductions (as proven in the quantum random oracle model) and instantiations, take into account quantum attackers, TESLA and qTESLA are considered post-quantum secure. Concurrently, the run-times for generating and verifying signatures of qTESLA are similar (or faster) than those of the RSA scheme. However, key and signature sizes of RSA are smaller than those of qTESLA. In order to protect both the theoretical signature schemes and their implementations against attacks, we analyze possible vulnerabilities against implementation attacks. In particular, cache-side-channel attacks resulting from observing the cache behavior and fault attacks, which recover secret information by actively disrupting the execution of an algorithm are focused. We present effective countermeasures for each implementation attack we found. Our analyses and countermeasures also influence the design and implementation of qTESLA. Although our schemes are considered (post-quantum) secure according to state-of-the-art LWE attacks, cryptanalysis of lattice-based schemes is still a relatively new field of research in comparison to RSA schemes. Hence, there is a lack of confidence in the concrete instantiations and their promised security levels. However, due to developments within the field of quantum computers, a transition to post-quantum secure solutions seems to be more urgently required than ever. To solve this dilemma, we present an approach to combine two schemes, e.g., qTESLA and the RSA signature scheme, so that the combination is secure as long as one of the two combined schemes is secure. We present several of such combiners to construct hybrid signature schemes and hybrid key encapsulation mechanisms to ensure both authenticity and confidentiality in our Public-Key Infrastructure (PKI). Lastly, we also demonstrate how to apply the resulting hybrid schemes in standards such as X.509 or TLS. To summarize, this work presents post-quantum secure candidates which can, using our hybrid schemes, add post-quantum security to the current classical security in our PKI.
The latest quantum computers have the ability to solve incredibly complex classical cryptography equations particularly to decode the secret encrypted keys and making the network vulnerable to hacking. They can solve complex mathematical problems almost instantaneously compared to the billions of years of computation needed by traditional computing machines. Researchers advocate the development of novel strategies to include data encryption in the post-quantum era. Lattices have been widely used in cryptography, somewhat peculiarly, and these algorithms have been used in both; (a) cryptoanalysis by using lattice approximation to break cryptosystems; and (b) cryptography by using computationally hard lattice problems (non-deterministic polynomial time hardness) to construct stable cryptographic functions. Most of the dominant features of lattice-based cryptography (LBC), which holds it ahead in the post-quantum league, include resistance to quantum attack vectors, high concurrent performance, parallelism, security under worst-case intractability assumptions, and solutions to long-standing open problems in cryptography. While these methods offer possible security for classical cryptosytems in theory and experimentation, their implementation in energy-restricted Internet-of-Things (IoT) devices requires careful study of regular lattice-based implantation and its simplification in lightweight lattice-based cryptography (LW-LBC). This streamlined post-quantum algorithm is ideal for levelled IoT device security. The key aim of this survey was to provide the scientific community with comprehensive information on elementary mathematical facts, as well as to address real-time implementation, hardware architecture, open problems, attack vectors, and the significance for the IoT networks.
The advent of quantum computing threatens to undermine current encryption methods significantly, especially those employed in mobile data transmission networks. Quantum algorithms can solve the computational challenges behind present public-key encryption methods like RSA (Rivest-Shamir-Adleman) and elliptic curve cryptography at a speedy rate. With mobile communication networks handling more and more sensitive information, the availability of secure authentication methods is increasingly important. This project proposes to investigate how mobile data communication systems can leverage post-quantum cryptographic (PQC) techniques to enhance authentication protocols. The research compares some NIST-standardized post-quantum cryptography candidates, i.e., lattice-based, code-based, hash-based, and multivariate polynomial cryptography, focusing on their usage in mobile environments. We establish a guideline for constructing PQC-improved authentication protocols, focusing on their quantum-resistance, computational cost, and appropriateness for resource-constrained mobile devices. Our analysis proves that the regulations successfully protect information’s secrecy, integrity, and authenticity in the post-quantum era. This has led to the development of future-proof, safe, and resilient mobile communication networks. PQC augmented authentication systems offer good resistance against quantum attacks while supporting acceptable performance on mobile devices, as evidenced by previous research. Mobile communication systems can achieve long-term security through PQC, thus safeguarding user data and critical infrastructure against potential adversaries that might employ quantum computing in the future.
A computer is recognized as a universal device that can simulate any other computational device, though it may take time. Cryptography is becoming more important as the Internet becomes more popular. When shopping online or using Internet banking, safe communication is crucial. However, traditional cryptography often relies on certain computational challenges, such as the RSA system, which is because of the complexity of factoring integers. This makes it vulnerable to advances in hardware, algorithms, and quantum techniques such as the Shor algorithm. In today's digital world, secure communication is essential. Quantum physics can change traditional cryptography. For example, an eavesdropper like Eve could record 2014 messages and, with future technology, decrypt them. Distribution of quantum keys (QKD) is a key application of quantum cryptography and promises unconditional communication security, unlike traditional methods that depend on unproven computational assumptions. Instead, QKD focuses on the physical laws. A challenge is the secure distribution of this key. In traditional methods, trusted couriers may be compromised unknowingly. QKD, introduced by Bennett and Brassard in 1984, involves Alice sending Bob photons with different polarization. They share their measurement results through a secure channel and generate a key while checking for interference. The onetime pad protocol ensures complete security if the key is not reused. QKD has become advanced enough for practical use. The article discusses cutting edge encryption methods including Lattice, Hash and Code-Based Cryptography, and their uses.