Sharif Digital Repository

Wide use of communication systems and transmission of huge data has increased the need for cryptographic and encoding systems with high speed operations and lower energy consumptions. Code based and joint encryption encoding schemes are examples of such systems, which enjoy simultaneously high performance and security against quantum computers. So far, there has not been developed any quantum algorithm which can solve any of the hard instances of coding theory based on which these cryptographic schemes have been designed. That is why such systems are called post quantum cryptosystems. The main disadvantage of such cryptosystems is large size the key which is to be stored or shared. In this... 

Polar codes were introduced by Arikan in 2009. These codes are the first family of codes that with low encoding complexity and successive cancellation decoder, can achieve the channel capacity. Polar codes, at first were implemented for channel coding, but in 2010 performance of these codes in binary and q-ary alphabet source was studied. It is shown that these codes can perform efficiently in channel coding and source coding. On the other hand, one of the most important continuous sources are Gaussian sources. Due to the importance of Gaussian sources and good performance of polar codes, we try to evaluate the performance of these codes in Gaussian sources. Note that, these codes have... 

Polar codes have received much attention to the extent that they are selected as a channel coding scheme in the 5G standard. The successive cancellation list (SCL) decoder suffers from high decoding Latency and limited Throughput due to its sequential decoding nature. Another polar decoding approach is the iterative belief propagation (BP) decoder which is inherently parallel and allows for better Decoding Latency and Throughput. However, its main drawback is an error-correction performance loss compared to the CRC-aided successive cancellation list (CA-SCL) decoder. From previous works, the CRC-aided belief propagation list (CA-BPL) decoder that benefits from the parallel structure of the... 

The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find practical schemes that approach these limits.Polar codes, recently invented by Arıkan, are the first practical codes that are known to achieve the capacity for a large class of channels. Their code construction is based on a phenomenon called “channel polarization”.
Since the performance of polar code degrades when the block length is small, several kinds of Reed – Solomon concatenation is considered in order to improve the... 

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... 

In modern wireless communication networks,that we have heterogeneous, asynchronous and ultra low latency networks and Due to the high processing power required by conventional cryptographic systems based on computational security, information theoritc security can play important role in the future development of these systems. Security in this case does not depend on the eavesdropper's computing power, but on the statistical independence between the main message and the received message of the eavesdropper. In recent years, polar codes have created new arenas, as they were the provable channel codes that could achieve capacity and reliability simultaneously. In addition, the clear structure,... 

In recent decades, the use of cryptography to ensure the security and confidentiality of telecommunications has become undeniable. In the meantime, public key primitives are one of the most important parts of cryptography. Given the advances in quantum processing and manufacturing technology of quantum computers in recent years, solving hard problems in the field of number theory, such as integer factorization and discrete logarithms, which are difficult to solve in conventional computers, are becoming possible. It is expected that the emergence of large-scale quantum computers will be able to solve these problems in a practical way using the Shor algorithm. Nowadays, most commonly used...