Learning with Errors is easy with quantum samples

Learning with Errors is one of the fundamental problems in computational learning theory and has in the last years become the cornerstone of post-quantum cryptography. In this work, we study the quantum sample complexity of Learning with Errors and show that there exists an efficient quantum learning algorithm (with polynomial sample and time complexity) for the Learning with Errors problem where the error distribution is the one used in cryptography. While our quantum learning algorithm does not break the LWE-based encryption schemes proposed in the cryptography literature, it does have some interesting implications for cryptography: first, when building an LWE-based scheme, one needs to be careful about the access to the public-key generation algorithm that is given to the adversary; second, our algorithm shows a possible way for attacking LWE-based encryption by using classical samples to approximate the quantum sample state, since then using our quantum learning algorithm would solve LWE

Public key cryptography in resource-constrained WSN

In this paper we present a detailed review of the works on public key cryptography (PKC) in wireless sensor networks (WSNs). In the early days of sensor networks, public key cryptography was thought to be completely unfeasible considering its computational complexity and energy requirements. By this time, several works have proved that the lightweight versions of many well-known public key algorithms can be utilized in WSN environment. With the expense of a little energy, public key based schemes could in fact be the best choice for ensuring data security in high-security demanding WSN applications. Here, we talk about the notion of public key cryptography in WSN, its applicability, challenges in its implementation, and present a detailed study of the significant works on PKC in WSN

Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

Improved Trial Division Algorithm by Lagrange?s Interpolation Function

Nowadays data communication over the internetgrowths the security risk on the side of receiver and transmitter. To reduce risk level, cryptography technique has been used which is based on aprivate and public key in disquiet of endorsement. The process of encryption and decryption improved the capacity of data security. Asymmetric cryptography technique provides renowned RSA public key cryptography technique. The success story of RSA algorithm depends on the prime factor. For the estimation of theprime factor used various mathematical functions. In this paper,Lagrange?s interpolation derivation for the estimation of aprime factoris used. The estimated prime factor is very complex and reduces the complexity of prime factor

Modern Cryptography Volume 1

This open access book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem. It aims to indicate what it is and why it is. It systematically simplifies and combs the theory and technology of lattice cryptography, which is the greatest feature of this book. It requires a good knowledge in algebra, number theory and probability statistics for readers to read this book. The senior students majoring in mathematics, compulsory for cryptography and science and engineering postgraduates will find this book helpful. It can also be used as the main reference book for researchers in cryptography and cryptographic engineering areas

An Empirical Investigation of Using ANN Based N-State Sequential Machine and Chaotic Neural Network in the Field of Cryptography

Cryptography is the exchange of information among the users without leakage of information to others. Many public key cryptography are available which are based on number theory but it has the drawback of requirement of large computational power, complexity and time consumption during generation of key [1]. To overcome these drawbacks, we analyzed neural network is the best way to generate secret key. In this paper we proposed a very new approach in the field of cryptography. We are using two artificial neural networks in the field of cryptography. First One is ANN based n-state sequential machine and Other One is chaotic neural network. For simulation MATLAB software is used. This paper also includes an experimental results and complete demonstration that ANN based n-state sequential machine and chaotic neural network is successfully perform the cryptography

A new public key cryptosystem based on IFS

Most public key encryption methods suffers from the inability to prove the difficulty of the algorithms, which summarizes under the category of mathematical problems that have inverses which are believed (but not proven) to be hard. The length and strength of the Cryptography keys are considered an important mechanism. The keys used for encryption and decryption must be strong enough to produce strong encryption. Fractals and chaotic systems have properties which have been extensively studied over the years, and derive their inherent complexity from the extreme sensitivity of the system to the initial conditions. In this paper a new cryptographic system based on Iterated Function Systems ( IFS) have been proposed to reduce the computation cost and increase the security for the public-key cryptography protocols. In the proposed public-key encryption algorithm, generate iterated function systems as a global public element, then its Hutchinson operator is used as a public key. To encrypt the plaintext with the receiver's public key we use one of the key agreement protocols to generate a shared private key that used to find the attractor of the IFS. The chaotic nature of the fractal functions ensures the security of the proposed public-key cryptosystem scheme

Some Facets of Complexity Theory and Cryptography: A Five-Lectures Tutorial

In this tutorial, selected topics of cryptology and of computational complexity theory are presented. We give a brief overview of the history and the foundations of classical cryptography, and then move on to modern public-key cryptography. Particular attention is paid to cryptographic protocols and the problem of constructing the key components of such protocols such as one-way functions. A function is one-way if it is easy to compute, but hard to invert. We discuss the notion of one-way functions both in a cryptographic and in a complexity-theoretic setting. We also consider interactive proof systems and present some interesting zero-knowledge protocols. In a zero-knowledge protocol one party can convince the other party of knowing some secret information without disclosing any bit of this information. Motivated by these protocols, we survey some complexity-theoretic results on interactive proof systems and related complexity classes.Comment: 57 pages, 17 figures, Lecture Notes for the 11th Jyvaskyla Summer Schoo