Sharif Digital Repository

In this thesis, we present a new identification protocol which is based on lattice problems. Lattice-based cryptographic algorithms are, in general, faster than those based on number theory. Moreover, instead of algorithms based on number theory problems, such as Factoring and Discrete Logarithm, lattice-based ones are resistant against quantum computers. In addition, lattice problems have worst-case/average-case hardness relation; so become suitable choices for cryptographic purposes. However, there are few lattice-based identification protocols which are efficient. The protocol introduced in this thesis, is statistical zero-knowledge which means no verifier, even computationally unbounded... 

In modern cryptography the main goal in symmetric cryptography algorithms is that the security of the protocol should be only dependent on the secrecy of key. Further, secret key agreement has a major role in perfect security. However, it is impossible to share a secrete key only by the use of a public channel and there must be another shared source. This source can be for instance random variables with some joint distribution (as in source model classical key distillation problem) or it can be some entangled quantum systems (as in quantum key distillation problem). The question here is that with the optimum efficiency, what is the maximum number of key bits that can be distilled from one... 

Post-quantum cryptography, as one of the newest groups of cryptographic algorithms, is thought to be secure against most sophisticated attacks by the groundbreaking quantum computers. Isogeny-based cryptography is an appealing contender among them due to its exceptional characteristics, especially the shortest public key in key encapsulation, encryption and decryption amid the other nominees of NIST post-quantum standard. However, its high computational complexity is a significant drawback. This research aims to increase the performance of isogeny-based cryptography in the most compute-intensive part, both in throughput and latency perspectives on GPUs and CPUs, which are the most widespread... 

Regarding to the emergence of quantum computers and advances in the large scale implementation of them, exploiting hard problems of coding theory is of great importance.This family of problems, like those of lattices, has an acceptable resistance against classic and quantum attacks. Thus, they can be replaced with hard problems in number theory and algebra. Increasing dominance of cyberspace made us highly dependent to it. Consequently, preparing tools and methods to mitigate future threats is necessary. Digital signatures constitute an important family of cryptographic primitives. Code-based digital signatures are mostly suffering from two main drawbacks: large public key and long time of... 

The amount of data over networks are increasing rapidly, and accordingly, smart devices are being encountered severe challenges by the advancement of security threats. In order to create safe communications among smart devices, employing public-key cryptography is needed. But, public-key and classic cryptography, such as RSA, have high computation complexities and are not resistant to quantum attacks. Due to mentioned reasons, using these types of cryptography algorithms in internet-of-things (IoT) devices is unreasonable. In the past decade, lattice-based cryptography has been one of the pioneer post-quantum cryptography members, which benefits from comparatively lower computational... 

Classic public key cryptographic systems are based on difficult mathematical problems that will lose their security with the advent of high-speed quantum computers. Isogeny-based cryptography is one of the five main methods in post-quantum cryptography, the hard problem of which is finding large-degree isogenies between elliptic curves. The most important advantage of isogeny-based protocols is the shorter public key length and the main problem is their low speed and low performance compared to other cryptographic systems. Due to the fact that these protocols are implemented on a finite field using basic operations, such as multiplication, squaring, addition, and subtraction, improving the... 

Lattice-based cryptography, as one of the main candidates for post-quantum cryptography, has attracted much attention along with cryptography researchers. That is mostly due to the fact that building large-scale quantum computers is possible within coming decades, which leads to a break-down in widely-used number-theoretic cryptographic schemes. Vulnerable cryptosystems include RSA, ECDSA, and ECDH, which are currently utilized everyday to secure cyberspace and digital communications. In this thesis, we focus on lattice-based and provably-secure authentication. Firstly, we propose three lattice-based authenticated encryption (AE) schemes. To the best of our knowledge, these are the first... 

Hyperledger Fabric is an open-source modular platform to launch permissioned-blockchains for use cases like banking and supply chains. This system uses the elliptic curve digital signature algorithm to authenticate transactions. The advent and progress of quantum computers have threatened the security of classical cryptographic schemes; therefore, the process of re- placing these schemes with post-quantum alternatives has gained considerable importance.This research intends to replace the elliptic curve digital signature algorithm with post-quantum digital signatures by using the algorithms passed to the third round of the National Institute of Science and Technologies (NIST) post- quantum... 

Public key encryption (PKE) cryptography plays a big role in securing communication channels of internet. The security of every PKE scheme is usually based on a hard problem that has no polynomial time solution using any computational structure. However, widely used classic PKE schemes such as RSA or ECC, are based on hard problems that have polynomial solutions using a quantum computer. Therefore, such PKE schemes will not be secure in post-quantum era. Among quantum-resistant schemes, lattice-based cryptography and especially learning with errors (LWE) problem have gained high attention due to their low computational complexity. In this thesis, different LWE-based cryptosystems are... 

Public-key cryptography is vital to secure digital communication. The classic instances of these cryptosystems are insecure against large-scale quantum computers. As a result, post-quantum cryptography has emerged as a replacement, which includes different categories. Isogeny-based schemes are one of the promising candidates mainly because of their smaller public key length. Due to high computational cost of such schemes, efficient implementations are significantly important. In this thesis, we have presented various solutions at three different abstraction layers. At the lowest layer, which deals with modular arithmetic, two hardware architectures are presented to perform modular... 

Quantum key distribution is one of the practical quantum information technologies in labo- ratories with existing equipments.In quantum key distribution protocols, the main challenge is the secrecy of key distribution. One of the new methods of quantum channel error esti- mation is the use of weak measurement. In this thesis, after introducing the main quantum key distribution protocols, we introduce weak measurement and sequential weak measure- ment concepts: the weak measurement methods are exployed to obtain the phase difference between two polarizations with high accuratly. It is also used for in line monitoring and error estimation parameters in some quantum key distribution protocols.... 

Quantum cryptography can provide complete security. Using the quantum mechanics postulates, we can achieve a provable security which is not possible in classical cryptography. When the first completely secure protocol for distributing key was introduced, it turned a great deal of attention toward quantum cryptography and researcher focused on finding quantum mechanical counterpart of other classical cryptographic protocols. Among these protocols, quantum secret sharing is one of the most useful and important ones. In this thesis, first we introduce the basic postulates of quantum mechanics. Then, we introduce some known quantum secret sharing protocols and discuss their properties and... 

Quantum computers can be used to process complex computations much more efficient than their classical counterparts. Cryptanalysis of classical ciphers is no exception to this rule. Most quantum cryptanalysis of symmetric ciphers is based on finding the periodicity, linear structure, and confidential information of the target algorithm. In this thesis, assuming that the attacker has access to the quantum computer, we propose a quantum method for deriving the appropriate differential characteristic of block ciphers, using Simon's quantum algorithm. It is worth noting that, unlike classical methods, where increasing the number of rounds of the target block cipher increases the complexity of...