Quantum Computing and Quantum Cryptography

The Rabin cryptosystem is an asymmetric cryptographic algorithm. Its security is based on the problem of integer factorization. Rabin cryptosystem has the advantage that the problem on which its security depends is proved to be as hard as factorization. The Rabin cryptosystem works in the domain of the odd primes which satisfy the criteria that

Received Dec 12, 2014 Revised Jan 20, 2015 Accepted Feb 26, 2015 The Rabin cryptosystem is an asymmetric cryptographic algorithm. Its security is based on the problem of integer factorization [4]. Rabin cryptosystem has the advantage that the problem on which its security depends is proved to be as hard as factorization [5]. Its minor disadvantage is that each output of the Rabin algorithm is generated by any of four possible inputs. If each output is a cipher text, extra complexity is required on decryption to identify which of the four possible inputs was the true plaintext. The process was published in January 1979 by Michael O. Rabin [2]. The Rabin cryptosystem was the first asymmetric cryptosystem where recovering the entire plaintext from the cipher text could be proven to be as hard as integer factorization. Keyword:

We developed a system to investigate resonant nonlinear optical interactions in acetylene molecules, confined in a hollow-core photonic crystal fiber (HC-PCF), using light injection through a low-loss splice from one end of the fiber, allowing us to work at low power. Electromagnetically induced transparency (EIT) was observed in the 1500 nm telecommunications window.

Secure and efficient data storage is needed in the cloud environment in modern era of information technology industry. In the present scenario the cloud verifies the authenticity of the cloud services without the knowledge of user's identity. The cloud provides massive data access directly through the internet. Centralized storage mechanism is followed here for effective accessing of data. Cloud service providers are normally acquires the software and hardware resources and the cloud consumers are avail the services through the internet access in lease basis. Cloud security is enhanced through cryptography technique applied to the cloud security to avoid vulnerability. The intractable computability is achieved in the cloud by using the public key cryptosystem. This paper proposed the approach of applying Hyper elliptic curve cryptography for data protection in the cloud with the small key size. The proposed system has the further advantage of eliminating intruder in cloud computing. Efficacy of the system is to provide the high security of the cloud data.

Secure and efficient data storage is needed in the cloud environment in modern era of information technology industry. In the present scenario the cloud verifies the authenticity of the cloud services without the knowledge of user's identity. The cloud provides massive data access directly through the internet. Centralized storage mechanism is followed here for effective accessing of data. Cloud service providers are normally acquires the software and hardware resources and the cloud consumers are avail the services through the internet access in lease basis. Cloud security is enhanced through cryptography technique applied to the cloud security to avoid vulnerability. The intractable computability is achieved in the cloud by using the public key cryptosystem. This paper proposed the approach of applying Hyper elliptic curve cryptography for data protection in the cloud with the small key size. The proposed system has the further advantage of eliminating intruder in cloud computing. Efficacy of the system is to provide the high security of the cloud data.

We define semi-commutative invertible masking structures which aim to capture the methodology of exponentiation-only protocol design (such as discrete logarithm and isogeny-based cryptography). We discuss two instantiations: the first is based on commutative group actions and captures both the action of exponentiation in the discrete logarithm setting and the action of the class group of commutative endomorphism rings of elliptic curves, in the style of the CSIDH key-exchange protocol; the second is based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct two oblivious transfer protocols using this new structure and prove that these UC-securely realise the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, by starting from one of these two protocols and using the compiler introduced by Döttling et al. (Eurocrypt 2020), we achieve the first fully UC-secure two-round OT protocol based on supersingular isogenies.

In this work we first define semi-commutative (invertible) masking structures which present a simple abstraction to capture the various examples of protocol design that are based on exponentiation-only style operations (such as discrete logarithm and isogeny based cryptography). We discuss two possible instantiations of our structure: The first is based on commutative group actions and captures both the action of exponentiation in the discrete logarithm setting and also the action of the class group of commutative endomorphism rings of elliptic curves, in the style of the CSIDH key-exchange protocol; the second is based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then design two oblivious transfer protocols using this structure and prove that they securely UC-realise the standard OT-functionality in the Random-Oracle-hybrid model against passive adversaries with static corruptions. This paper thus i...

This is a brief introduction to the D2-KFAB Theory, which stands for ‘Koopman Feynman-Kac AdS/CFT Boltzmann D2-Brane on KAM Tori DBI Action’. The D2-KFAB is a math, physics, and AI-machine learning unified theoretical framework. The theory has been constructed over the last ten years and developed in a series of papers and presentation talks primarily for the Society of Industrial and Applied Mathematics (SIAM) https://www.siam.org/.

This theory is a simplified consolidation that adds to research on stochastic PDEs, chaos/complexity, quantum gravity/string theory, gravitational waves/cosmic strings, fluid dynamics, plasma physics, fusion energy/ion propulsion, artificial intelligence/neural networks, metamaterials cloaking/singularities, robotics, quantum computing/cryptography, econometrics/stock markets.

In this fast transforming world finance and money is also transforming on a high note.Digitalized strength and other innovative systems and instruments are creating new platforms for financial traction who rectify and assume your transaction. Crypto is one such platform where transactions are secured and verified trustfully. Here in this paper, we will come to know how mathematics has enhanced the word of cryptography.In this paper we are going to study about role of mathematics in crypto text, encryption, symmetric key, stream, block cypher, asymmetric key and functions along with hash function,.Crypto key management andEfficient implementation. This paper provides a pure knowledge of application of mathematics in cryptography and how mathematics has enhanced in a truly different way.

The cryptography is the branch of Cryptology. It is a combination of mathematics and computer Science. It is the study of obscuring information in cyberspace. Cipher is a set of algorithm which comprise of encryption and decryption. The cipher paly important role in modern technology. The technologies involving communication including the Internet, Mobile Phones, Digital Television, and ATM machine rely on cipher in order to maintain security and privacy. Thinking about aforesaid importance of cipher in cryptography, in this article, we have designed a smallest cipher which may be efficient in RFID chips. The smallest cipher has been comprised of five mathematical operation: Exponentiation, Multiplication, Addition, Subtraction and Division based on systematic study of classical cipher. The proposed cipher is a keyless cipher, but it is very efficient in secret information passing.

In this fast transforming world finance and money is also transforming on a high note.Digitalized strength and other innovative systems and instruments are creating new platforms for financial traction who rectify and assume your transaction. Crypto is one such platform where transactions are secured and verified trustfully. Here in this paper, we will come to know how mathematics has enhanced the word of cryptography.In this paper we are going to study about role of mathematics in crypto text, encryption, symmetric key, stream, block cypher, asymmetric key and functions along with hash function,.Crypto key management andEfficient implementation. This paper provides a pure knowledge of application of mathematics in cryptography and how mathematics has enhanced in a truly different way.

The cryptography is the branch of Cryptology. It is a combination of mathematics and computer Science. It is the study of obscuring information in cyberspace. Cipher is a set of algorithm which comprise of encryption and decryption. The cipher paly important role in modern technology. The technologies involving communication including the Internet, Mobile Phones, Digital Television, and ATM machine rely on cipher in order to maintain security and privacy. Thinking about aforesaid importance of cipher in cryptography, in this article, we have designed a smallest cipher which may be efficient in RFID chips. The smallest cipher has been comprised of five mathematical operation: Exponentiation, Multiplication, Addition, Subtraction and Division based on systematic study of classical cipher. The proposed cipher is a keyless cipher, but it is very efficient in secret information passing.

In this fast transforming world finance and money is also transforming on a high note.Digitalized strength and other innovative systems and instruments are creating new platforms for financial traction who rectify and assume your transaction. Crypto is one such platform where transactions are secured and verified trustfully. Here in this paper, we will come to know how mathematics has enhanced the word of cryptography.In this paper we are going to study about role of mathematics in crypto text, encryption, symmetric key, stream, block cypher, asymmetric key and functions along with hash function,.Crypto key management andEfficient implementation. This paper provides a pure knowledge of application of mathematics in cryptography and how mathematics has enhanced in a truly different way.

‎In this paper‎, ‎we propose some Diffie-Hellman type key exchange protocols using isogenies of elliptic curves‎. ‎The first method which uses the endomorphism ring of an ordinary elliptic curve $ E $‎, ‎is a straightforward generalization of elliptic curve Diffie-Hellman key exchange‎. ‎The method uses commutativity of the endomorphism ring $ End(E) $‎. ‎Then using dual isogenies‎, ‎we propose a second method‎. ‎This case uses the endomorphism ring of an elliptic curve $ E $‎, ‎which can be ordinary or supersingular‎. ‎We extend this method using isogenies between two elliptic curves $ E $ and $ E' $‎. ‎Our methods have the security level of that of [D‎. ‎Jao and L‎. ‎De Feo‎, ‎Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies‎,  J‎. ‎Math‎. ‎Cryptol. 8 (2014)‎, ‎no‎. ‎3‎, ‎209--247]‎, ‎with the advantage of transmitting less information between two parties‎.

Information security and privacy in healthcare IT have been a longstanding challenge in recent years. Technologies like data mining, private database, Role based access control, encryption etc. attain the goal at some extent but don’t provide a solution to resolve every aspect. Considering the extremely sensitive nature of medical records, in any attempt to transmit the data over the network; we need to make sure that any third party cryptanalyst can’t be able to access, modify or even understand the encrypted document sent over the network. This growing privacy and security needs in electronic-health records is the motivation for our approach. In this paper, we propose an approach for integration and exchange of medical records over the network in a service oriented driven framework using HL7 standard that provides an end-to-end security.

Cloud Computing is a way to enhance the facility or add capabilities with liveliness without investing in new infrastructure, training new human resources, or licensing latest software. It extends Information Technology’s (IT) existing capabilities. In the preceding few years, cloud computing has full-grown from being a promising business concept to one of the fast growing sector of the IT industry. But as more and more information on individuals and companies are placed in the cloud, concerns are beginning to raise about just how secure cloud environment it is. Despite of all the build-up surrounding the cloud, enterprise customers are still unwilling to deploy their business in the cloud. Security is one of the major issues which reduces the growth of cloud computing and complications with data privacy and data protection continue to outbreak the market. Due to storing data on cloud there is an issue of data security. To ensure the correctness of user’s data in the cloud, we recom...

We analyse the role of degree of entanglement for Vaidman's game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be always helpful in winning a game as opposed to the classical strategies. We further find the conditions under which quantum strategies are always helpful in achieving higher winning probability in the game in comparison to classical strategies. Moreover, we show that a special class of W states can always be used to win the game using quantum strategies irrespective of the degree of entanglement between the three qubits. Our analysis also helps us in comparing the Vaidman's game with the secret sharing protocol. Furthermore, we propose a new Vaidman-type game where the rule maker itself is entangled with the other two players and acts as a facilitator to share a secret key with the two players. For practical purposes, the analysis is extended to study the proposed game under noisy conditions. In addition, the results obtained here are also generalized for multi-qubit games.

We developed a system to investigate resonant nonlinear optical interactions in acetylene molecules, confined in a hollow-core photonic crystal fiber (HC-PCF), using light injection through a low-loss splice from one end of the fiber, allowing us to work at low power. Electromagnetically induced transparency (EIT) was observed in the 1500 nm telecommunications window.

We developed a system to investigate resonant nonlinear optical interactions in acetylene molecules, confined in a hollow-core photonic crystal fiber (HC-PCF), using light injection through a low-loss splice from one end of the fiber, allowing us to work at low power. Electromagnetically induced transparency (EIT) was observed in the 1500 nm telecommunications window.

In this paper we analyze the (im)possibility of the exact distinguishability of orthogonal multipartite entangled states under restricted local operation and classical communication. Based on this local distinguishability analysis we propose a new scheme for quantum secret sharing (QSS). Our QSS scheme is quite general and cost efficient compared to other schemes. In our scheme no joint quantum operation is needed to reconstruct the secret. We also present an interesting (2, n)-threshold QSS scheme, where any two cooperating players, one from each of two disjoint groups of players, can always reconstruct the secret. This QSS scheme is quite uncommon, as most (k, n)-threshold schemes have the restriction k ≥ ⌈ n 2 ⌉.

The main purpose of the presented paper is to establish a secure way by integrating the biological characteristic as a key with cryptographic applications. A binary string is generated reliably from genuine fingerprint conventions. That key is generated from a subject’s fingerprint image with the aid of SDK, which do not reveal the key. The reproduction of that key depends on the equivalent biometric fingerprint. That’s why the general key distribution problem is always refer to the task of distributing secret keys between communicating parties to provide security properties such as secrecy and authentication. A novel technique is introduced to exchange personal biometric fingerprint (payload) as a symmetric key in secrecy using Secure Hash Algorithm 1 which is working as a cryptographic hash function one way to produce 20-bytes hash value known as a message digest. Then the asymmetric cryptosystem is used to transport that key in a safe way to the other parties. Once they have the ...

Article history: Received: 25/01/2020 Revised: 31 / 01/2020 Accepted: 01/02/2020 Privacy and data security is one of the most important aspects that need to be addressed, especially in this digital age where all desktop and mobile computing devices can be connected to one another in a virtual world that causes virtually impossible to protect the message to its destination. The purpose of this study is a modification of the Playfair cipher algorithm and caesar cipher with the postal code of the city, aims to produce a ciphertext that is more complex and not easily solved. In this penelian also implement LSB steganography method so that the message content more secure and not readily known by those who do not have an interest. From the test results of this study showed that by modifying the Playfair cipher algorithm and caesar cipher with city postal code in the encoding, produce ciphertext more complicated to be returned to the original message by parties who have no interest. Applyi...

The 5-qubit quantum computer prototypes that IBM has given open access to on the cloud allow the implementation of real experiments on a quantum processor. We present the results obtained in five experimental tests performed on these computers: dense coding, quantum Fourier transforms, Bell's inequality, Mermin's inequalities (up to n = 5) and the construction of the prime state |p 3. These results serve to assess the functioning of the IBM 5Q chips.

The use of electronic medical record (EMR) system is gaining attention in the healthcare sectors around the world, and its acceptability threatened by the security of patients’ information. Hence, the need to carry out study on efficient way(s) of protecting the information on EMR so that when even accessed it will remain incomprehensible except the approval is granted by the concern patient. The proposed solution for the protection of patients’ information on electronic medical record EMR in this research was based on secondary data. Basically, one of the online database that were given particular attention was the software Open Medical System (OpenMRS). Experimental results obtained from three different asymmetric encryption algorithms show that Rivest-Shamir-Adleman (RSA) was the most efficient among the selected encryption algorithms based on the performance keys, and it was used to build an email notification system prototype for the protection of patients medical records. The ...

Cryptography is the practise and study of techniques for secure communication in the presence of third parties. The necessity and the fact that exchanged messages are exposed to other people during the transmission promoted the creation of encryption systems, enabling just the recipients to interpret the exchanged information. In this paper, a particular cryptosystem called Rabin Cryptosystem is presented and analysed with the help of Chinese Reminder Theorem. Also, redundancy schemes for decryptions technique is mentioned and some basic mathematical concepts is explained and finally compared with RSA cryptosystem in terms of security and efficiency.

I hereby declare that this research monograph becomes the property of Md. Shamim Hossain Biswas and to be placed at the worldwide database access library for future cryptographic researchers and also be available Online. Md. Shamim Hossain Biswas is the owner of this Monograph and own all copyrights of the Work. IJSRP acts as publishing partner and author will remain owner of the content. Copyright©2020, All Rights Reserved No part of this Monograph may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as described below, without the permission in writing of the Author & publisher. Copying of content is not permitted except for personal and internal use, to the extent permitted by national copyright law, or under the terms of a license issued by the national Reproduction Rights Organization.

The cryptography is the branch of Cryptology. It is a combination of mathematics and computer Science. It is the study of obscuring information in cyberspace. Cipher is a set of algorithm which comprise of encryption and decryption. The cipher paly important role in modern technology. The technologies involving communication including the Internet, Mobile Phones, Digital Television, and ATM machine rely on cipher in order to maintain security and privacy. Thinking about aforesaid importance of cipher in cryptography, in this article, we have designed a smallest cipher which may be efficient in RFID chips. The smallest cipher has been comprised of five mathematical operation: Exponentiation, Multiplication, Addition, Subtraction and Division based on systematic study of classical cipher. The proposed cipher is a keyless cipher, but it is very efficient in secret information passing.

We developed a system to investigate resonant nonlinear optical interactions in acetylene molecules, confined in a hollow-core photonic crystal fiber (HC-PCF), using light injection through a low-loss splice from one end of the fiber, allowing us to work at low power. Electromagnetically induced transparency (EIT) was observed in the 1500 nm telecommunications window.

RSA [1] is one of the mostly used cryptosystem in securing data and information. Though, it has been recently discovered that RSA has some weaknesses and in advance technology, RSA is believed to be inefficient especially when it comes to decryption. Thus, a new algorithm called Multi prime RSA, an extended version of the standard RSA is studied. Then, a modification is made to the Multi prime RSA where another keys is shared secretly between the receiver and the sender to increase the securerity. As in RSA, the methodology used for modified Multi-prime RSA also consists of three phases; 1. Key Generation in which the secret and public keys are generated and published. In this phase, the secrecy is improved by adding more prime numbers and addition of secret keys. 2. Encryption of the message using the public and secret keys given. 3. Decryption of the secret message using the secret key generated. For the decryption phase, a method called Chinese Remainder Theorem is used which helps to fasten the computation. Since Multi prime RSA use more than two prime numbers, the algorithm is more efficient and secure when compared to the standard RSA. Furthermore, in modified Multi prime RSA another secret key is introduced to increase the obstacle to the attacker. Therefore, it is strongly believed that this new algorithm is better and can be an alternative to the RSA.

In this paper, we develop a quantum key distribution protocol based on the Greenberger-Horne-Zeilinger states (GHZs). The particles are exchanged among the users in blocks through two steps. In this protocol, for three-particle GHZs three keys can be simultaneously generated. The advantage of this is that the users can select the most suitable key for communication. The protocol can be generalized to N users to provide N keys. The protocol has two levels for checking the eavesdroppers. Moreover, we discuss the security of the protocol against different attacks.

We propose a new quantum protocol to teleport an arbitrary unknown Nqubit entangled state from a sender to a fixed receiver under the control of M (M < N) controllers. In comparison with other existing protocols, ours is more economical and more feasible. The quantum resource required is just M Greenberger-Horne-Zeilinger trios plus (N − M) Einstein-Podolsky-Rosen pairs. The techniques required are only N Bell measurements by the sender, a von Neumann measurement by a controller and N single-qubit transformations by the receiver. The rule for the receiver to reconstruct the desired state is derived explicitly in the most general case.

The cryptography is the branch of Cryptology. It is a combination of mathematics and computer Science. It is the study of obscuring information in cyberspace. Cipher is a set of algorithm which comprise of encryption and decryption. The cipher paly important role in modern technology. The technologies involving communication including the Internet, Mobile Phones, Digital Television, and ATM machine rely on cipher in order to maintain security and privacy. Thinking about aforesaid importance of cipher in cryptography, in this article, we have designed a smallest cipher which may be efficient in RFID chips. The smallest cipher has been comprised of five mathematical operation: Exponentiation, Multiplication, Addition, Subtraction and Division based on systematic study of classical cipher. The proposed cipher is a keyless cipher, but it is very efficient in secret information passing.

M.S.H. Biswas crypto-intensive techniques in combination of Encryption algorithm, Signature generation algorithm, Signature verification algorithm and Decription algorithm. Michael O. Rabin Signature scheme uses random padding to validate signature. Analogously the proposed techniques uses same padding system including additional quotient and residuum. The only difference is that Rabin signature is pair or triple in some special cases but proposed model uses forefold signature system. Michael O. Rabin Cryptosystem can generate same ciphertext form different plaintext as well as multiple plaintext from single cyphertext. To solve those issues, i designed a new cryptosystem "A mathematical model for ascertaining same ciphertext generated from distinct plaintext in Michael O. Rabin Cryptosystem". But it did not have authentication system to verify sender and valid message because there was no signature generation facility.In this article, i have designed a new signature algorithm in combination with previous techniques and Michael O. Rabin public key Signature scheme. Receiver can decipher secret message from sender's signature. The proposed crypto intensive technique uses two times security key by slightly altering Diffie-Hellman key exchange protocol. The advantage of proposed crypto intensive technique is that the sender generate signature using encrypted text and intended receiver can retrieve plaintext from signature through signature verification system.The proposed crypto teachniques secure against man-in-the-middle attack. It is unforgeable while Rabin's signature is forgeable in forgery attack.

We demonstrate the possibility of controlling the success probability of a secret sharing protocol using a quantum cloning circuit. The cloning circuit is used to clone the qubits containing the encoded information and en route to the intended receipients. The success probability of the protocol depends on the cloning parameters used to clone the qubits. We also establish a relation between the concurrence of initially prepared state, entanglement of the mixed state received by the receivers after cloning scheme and the cloning parameters of cloning machine. * satya@iitj.ac.in

Michael O. Rabin Cryptosystem can generate same ciphertext form different plaintext as well as multiple plaintext from single cyphertext. There are a number of techniues to reveal original plaintext. But none of them can seperate same cyphertext against each plaintext generated from modular reduction arithmetic. If question arises about how one can distinguish particular ciphertext against each plaintext, to answer those questions, I design a new mathematical model for identifying same ciphertext against each plaintext and it also facilitates message encryption and decryption. The proposed mathematical model constructiond based on quadratic root of quadratic residue, quadratic quotient, floor function and absolute value counting in order to identify the ciphertext against the plaintext. In particular. When same number of residues generated from multiple plaintext applying modular reduction arithmetic. The proposed crypto intensive technique uses symmetric key using Diffie-Hellman key exchange protocol. The advantage of proposed crypto intensive technique is intended receiver getting only one plainvalue distinguishing the ciphertext against the plaintext. The proposed crypto teachnique requires less time complexity and probabily secure against man-in-the-middle, chosen plaintext and cyphertext attack.

Cryptography is the practise and study of techniques for secure communication in the presence of third parties. The necessity and the fact that exchanged messages are exposed to other people during the transmission promoted the creation of encryption systems, enabling just the recipients to interpret the exchanged information. In this paper, a particular cryptosystem called Rabin Cryptosystem is presented and analysed with the help of Chinese Reminder Theorem. Also, redundancy schemes for decryptions technique is mentioned and some basic mathematical concepts is explained and finally compared with RSA cryptosystem in terms of security and efficiency.

Abstract A detailed analysis has showed that the quantum secret sharing protocol based on the Grover algorithm (Phys Rev A, 2003, 68: 022306) is insecure. A dishonest receiver may obtain the full information without being detected. A quantum secret-sharing protocol is ...

In this slides I have tried to define secret sharing mathematically and discussed the classical secret sharing scheme named (k,n) threshold scheme given by Adi Shamir (Commun. ACM 22, 612) in 1979 and in continuation the QSS scheme was prsented here which was given by Hilery et. al. ( Phys. Rev. A 59, 1829) in 1999.

We discuss (im)possibility of the exact cloning of orthogonal but genuinely entangled three qubit states aided with entangled ancila under local operation and classical communication. Whereas any two orthogonal GHZ states taken from the canonical GHZ basis, can be cloned with the help of a known GHZ state, surprisingly we find that no two W states can be cloned by using any known three qubit (possibly entangled) state as blank copy.

We introduce a problem of distinguishing between two quantum states as a new underlying problem to build a computational cryptographic scheme that is ”secure” against quantum adversary. Our problem is a natural generalization of the distinguishability problem between two probability distributions, which are commonly used in computational cryptography. More precisely, our problem QSCDff is the computational distinguishability problem between two types of random coset states with a hidden permutation over the symmetric group. We show that (i) QSCDff has the trapdoor property; (ii) the average-case hardness of QSCDff coincides with its worst-case hardness; and (iii) QSCDff is at least as hard in the worst case as the graph automorphism problem. Moreover, we show that QSCDff cannot be efficiently solved by any quantum algorithm that naturally extends Shor’s factorization algorithm. These cryptographic properties of QSCDff enable us to construct a public-key cryptosystem, which is likely to withstand any attack of a polynomial-time quantum adversary.