NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.

Vortrag ueber das Warum und Wie der Kryptografie mit oeffentlichen Schluesseln am Beispiel von GNU Privacy Guard

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: NTRU; cryptography; scalable multiplier; unified multiplier; Montgomery multiplier. Includes bibliographical references (p. 85-88).

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

published_or_final_version / abstract / toc / Computer Science / Master / Master of Philosophy

published_or_final_version / abstract / toc / Computer Science and Information Systems / Master / Master of Philosophy

The online trading is growing widely day by day, which makes safety the biggest concern while carrying out trading by electronic means. As many other operations can be done with digital environment and internet, operation that provides identity validation should also be added to the digital environment. When data are transferred, the user should make sure that there are no changes in the original data while transferring them from sender to receiver. And it has also become necessary to authenticate the users often to ensure security and to avoid fraud. There are lot of different ways of online identification, in which digital signature is considered to be one of the powerful way of authentication. So, the online user use digital signature to authenticate the sender and to maintain the integrity of the document sent. In this paper, a study is carried out to identify the usage of digital signature and the perspective of people towards it in developed and developing countries and a survey is taken to support the theory.

Nowadays all existing public key cryptosystems are classified into three categories relied on different mathematical foundations. The first one is based on the difficulty of factoring the product of two big prime numbers. The representatives are the RSA and the Rabin cryptosystems. The second one such as the ElGamal cryptosystem is based on the discrete logarithm problem. The last one is based on the NP-completeness of the knapsack problem. The first two categories survived crypto attacks, whereas the last one was broken and there has been no attempt to use such a cryptosystem. In order to save the last category, Kiriyama proposed a new public key cryptosystem based on the non-linear knapsack problem, which is an NP-complete problem. Due to the non-linear property of the non-linear knapsack problem, this system resists all known attacks to the linear knapsack problem. Based on his work, we extend our research in several ways. Firstly, we propose an encrypted secret sharing scheme. We improve the security of shares by our method over other existing secret sharing schemes. Simply speaking, in our scheme, it would be hard for outsiders to recover a secret even if somehow they could collect all shares, because each share is already encrypted when it is generated. Moreover, our scheme is efficient. Then we propose a multiple identities authentication scheme, developed on the basis of the non-linear knapsack scheme. It verifies the ownership of an entity's several identities in only one execution of our scheme. More importantly, it protects the privacy of the entities from outsiders. Furthermore, it can be used in resource-constrained devices due to low computational complexity. We implement the above schemes in the C language under the Linux system. The experimental results show the high efficiency of our schemes, due to low computational complexity of the non-linear knapsack problem, which works as the mathematical foundation of our research.

NTRU is a fast public-key cryptosystem that is constructed using polynomial rings with integer coefficients. We present ETRU, an NTRU-like cryptosystem based on the Eisenstein integers. We discuss parameter selection and develop a model for the probabilty of decryption failure. We also provide an implementation of ETRU. We use theoretical and experimental data to compare the security and efficiency of ETRU to NTRU with comparable parameter sets and show that ETRU is an improvement over NTRU in terms of security.