Small Key Size Research Articles

Secure and Robust Telemedicine using ECC on Radix-8 with Formal Verification

The scalar multiplication techniques used in Elliptic curve cryptography (ECC) are having the scope for gaining the computation efficiency. This is possible through the reduction of precomputed operations. Finding the more efficient technique compares to the most recent or efficient one is a research gap for all schemes. The manuscript presents an application oriented work for Telemedicine using ECC. It is based on robust application on reduced computational complexity. The methodology we apply for the same is Scalar Multiplication without precomputation on Radix-8. Introduced software and the hardware performance are reporting a big advantage over all the related proposed techniques. The reason to cover this problem is to provide a path on a fascinating area of ECC on a smaller key size be applicable for all applications on a same level of security strengths. The smaller length key gives the higher speed and shorter clock cycle to initiate the operation.

A non-commutative cryptosystem based on quaternion algebras

We propose BQTRU, a non-commutative NTRU-like cryptosystem over quaternion algebras. This cryptosystem uses bivariate polynomials as the underling ring. The multiplication operation in our cryptosystem can be performed with high speed using quaternions algebras over finite rings. As a consequence, the key generation and encryption process of our cryptosystem is faster than NTRU in comparable parameters. Typically using Strassen’s method, the key generation and encryption process is approximately 16 / 7 times faster than NTRU for an equivalent parameter set. Moreover, the BQTRU lattice has a hybrid structure that makes inefficient standard lattice attacks on the private key. This entails a higher computational complexity for attackers providing the opportunity of having smaller key sizes. Consequently, in this sense, BQTRU is more resistant than NTRU against known attacks at an equivalent parameter set. Moreover, message protection is feasible through larger polynomials and this allows us to obtain the same security level as other NTRU-like cryptosystems but using lower dimensions.

A New variant of the McEliece cryptosystem based on the Smith form of convolutional codes

ABSTRACTIn this article, the authors propose a new version of the McEliece cryptosystem based on the Smith form of convolutional codes. They use the Smith form to hide a part of the code in the public matrix, and they leave the other part secret. The secret part will then be used for decryption. They hide this part by multiplying it on the left by a random matrix, and they add a random matrix which has a few conditions. Their scheme has a small public key size compared to the original McEliece scheme and resists the unique decoding attack against convolutional structure presented at the conference PQCrypto 2013 by Landais and Tillich. Further, the exhaustive search attack is infeasible on their system.

Polar code‐based secure channel coding scheme with small key size

In this study, the secret polar encoding and secret successive cancellation decoding algorithms are introduced; with these algorithms, secure and efficient communication can be enhanced between the honest parties. Also, the key size of the proposed polar code-based secure channel coding system is reduced significantly compared to the existing systems. To decrease the key size, the authors employ the three following methods: (i) a new approach is proposed to save some bit-channel indices instead of saving the generator matrix of the used polar code; (ii) the permutation and scrambling matrices are not used in this scheme; and (iii) by the help of the properties of polar codes, it does not need to save any vector as part of secret key set to generate an error vector. Moreover, the security analyses demonstrate that this system is resistant against conventional attacks on symmetric-key code-based cryptosystems. It means that reducing the key size of the proposed polar code-based scheme does not affect its security level.

SECURE HYBRID ENCRYPTION USING ECC IN CLOUDS

The evolution of the cloud computing furnishes a better way for the data storage. ABE with delegation is accustomed for accessing the data and keep it confidential. But this scheme faces some limitations like the cloud servers can replace the cipher text with some malignant intent. They may also cheat the eligible users as unauthorized ones. The cloud servers even face external threats like the security attacks. So, to protect against the security attacks and to preserve the data integrity in the cloud, a hybrid encryption with VD scheme is proposed by Xu et al. Even this scheme faces the challenges like having larger keys, more computational time and vulnerability to man-in-the-middle attacks. A secure Hybrid Encryption using ECC in clouds is proposed to overcome these problems. The application of Elliptic Curve Cryptography and its algorithms in the proposed work provides a greater security because of the Elliptic Curve Discrete Logarithm Problem. The proposed work ensures greater security with the aid of a smaller key size. It also ensures less computational time, less memory and communication bandwidth

Minimization of mean square error for improved euler elliptic curve secure hash cryptography for textual data

Elliptic Curve Cryptography is a currently pursued research topic to be used in the security system that enhances the performance of unexpected character at the time of decryption process. In comparison with the traditional cryptosystems, for example, the RSA i.e. Rivest Shamir Algorithm, an Elliptic Curve Cryptography (ECC) provides equal security with the use of smaller key sizes, which produces faster computations, power usage is lowered, as well as memory usage and bandwidth variations are less. In the proposed technique, Euler based Elliptic curve secure hash (ECSH-Euler) that overcome the problem of Euler Totient function based on fixed key for prime number coefficient corresponding matrix based on the plain text’s ASCII values is proposed. Values in a pair are defined as input for the hash key in the ECC. This new technique removes the need for the costly operation where mapping is done and the where there exists a requirement of sharing the same ASCII matrix for both purposes that are encryption and decryption .Both, the lookup table that is common between the sender - receiver along with the equation provides more security due to the reason of producing a numerical solution to a problem of initial value. Thus in this, a comparison of existing ECC and ECSH-Euler is also shown that resulted in minimization of RMSE for our proposed technique, which is simulated in MATLAB-2014Ra tool.

Optimized Layout of a Medium-Type Model for Korean Soft Keyboards in Smart Phones

Medium-type Korean soft keyboards for smart phones are required currently and are considered an optimized keyboard type that combines a QWERTY-type keyboard, which suffers from small key size, and a 12-key keypad, which require a troublesome input method. In this paper, we will look at the design of medium-type Korean keyboards consisting of 3 rows. The models are classified as having one of the following layouts: (A) a lattice layout with a backspace, (B) a lattice layout with a backspace and a shift (auxiliary) key, and (C) a tilt layout. The models can also be classified as 6-column, 7-column, and 8-column models. The lattice layout of the 7-column model is developed representatively (as a prototype), in which 14 keys for 14 consonants and 6 keys for 10 vowels are arranged. An experiment is performed to obtain the difference in typing times between a QWERTY-type soft keyboard and the proposed model; the p-value of the results is 0.00114. Therefore, the developed model is significantly more effective than the QWERTY-type model. Digits and symbol characters are allocated to the shoulder positions and are accessed using the long-pressing input method.

Homomorphic MAC from Algebraic One-Way Functions for Network Coding with Small Key Size

Homomorphic MAC from Algebraic One-Way Functions for Network Coding with Small Key Size

Elliptic Curve Cryptosystem in securing Communication across Unsecure Channel

In the present day, exchanging information is the essential of successful business in our society. Securing the information from unauthorized individuals as well as unauthorized access is more essential. Cases of hacking bank accounts, stealing credit card numbers and decoding secret information are common occurrence. With the rapid grow of internet technology and increasing computational power of computer, securing privilege information against unauthorized access is a source of concern to the business managers. Different organisation use different methods to secure sensitive information. Most of these methods have not provided the desired result. This paper proposes the use of Elliptic Curve Cryptography (ECC) over finite fields to send and receive information in an unsecure channel without jeopardizing the security of the information. The basisof using ECC is because there is no known technique of finding solution of discrete logarithm problem, in a reasonable time, on a properly chosen elliptic curve. ECC has advantagesof smaller key sizes, faster computations, reductions in processing power, less storage space and low bandwidth rate consumption.In this paper, group theory, elliptic curves, finite fields and ECC encoding were explained.

Nonlinear Cryptosystem Based on QC-LDPC Codes for Enhanced Security and Reliability with Low Hardware Complexity and Reduced Key Size

The main issues to be addressed in resource limited devices are security, reliability and hardware complexity. Cryptosystems that combine encryption and error correction in a single step can offer a good solution to meet these issues. In this work, a nonlinear cryptosystem based on structured Low-Density Parity-Check code that offers small key size, low hardware complexity and high security against differential type of attack is proposed. The method adopted to introduce nonlinearity in a cryptosystem plays a key role in deciding the hardware complexity and security of the overall system. The work adopts a method for generating nonlinear function using maximum length Cellular Automata, so that enhanced security can be attained without going for a complex hardware structure. Also a light weight stream cipher is adopted for generating random error vectors for encryption and addition of intentional noise in such a way that the security is increased by a large margin at a low hardware cost. Different permutation matrices are generated for different message blocks for achieving good degrees of freedom with reasonable key size. Analysis shows that the proposed system provides high security with smaller key size and lower hardware complexity when compared with a nonlinear cryptosystem called Error Correction Based Cipher.

A New Key Management Scheme for Wireless Sensor Networks using an Elliptic Curve

Objectives: Our objective is to design a new key management scheme for wireless sensor networks. Methods/Analysis: The paper describes an effective and novel key management scheme for wireless sensor networks using elliptic curve public key cryptosystem. The proposed key management scheme uses multiple private keys and a pair of public keys. Findings: The proposed key management scheme was tested for performance evaluation using various elliptic curves of different parameters. The experimental results showed that our scheme performed well in spite of using multiple private keys and a pair of public keys. Applications/Improvements: The proposed key management scheme can be used in wireless sensor networks as elliptic curve cryptosystem uses small key length or size in contrast to other public key cryptosystems.

Decoding the Tensor Product of MLD Codes and Applications for Code Cryptosystems

For the practical application of code cryptosystems such as McEliece, it is necessary that the code used in the cryptosystem should have a fast decoding algorithm. On the other hand, the code used must be such that finding a secret key from a known public key would be impractical with a relatively small key size. In this connection, in the present paper it is proposed to use the tensor product \( C_1 \otimes C_2 \) of group \(\textrm{MLD}\) codes \( C_1 \) and \( C_2 \) in a McEliece-type cryptosystem. The algebraic structure of the code \( C_1 \otimes C_2 \) in the general case differs from the structure of the codes \( C_1 \) and \( C_2 \), so it is possible to build stable cryptosystems of the McEliece type even on the basis of codes \( C_i \) for which successful attacks on the key are known. However, in this way there is a problem of decoding the code \( C_1 \otimes C_2 \). The main result of this paper is the construction and justification of a set of fast algorithms needed for decoding this code. The process of constructing the decoder relies heavily on the group properties of the code \( C_1 \otimes C_2 \). As an application, the McEliece-type cryptosystem is constructed on the code \( C_1 \otimes C_2 \) and an estimate is given of its resistance to attack on the key under the assumption that for code cryptosystems on codes \( C_i \) an effective attack on the key is possible. The results obtained are numerically illustrated in the case when \( C_1 \), \( C_2 \) are Reed--Muller--Berman codes for which the corresponding code cryptosystem was hacked by L. Minder and A. Shokrollahi (2007).

BSEA: A Blind Sealed-Bid E-Auction Scheme for E-Commerce Applications

Due to an increase in the number of internet users, electronic commerce has grown significantly during the last decade. Electronic auction (e-auction) is one of the famous e-commerce applications. Even so, security and robustness of e-auction schemes still remain a challenge. Requirements like anonymity and privacy of the b i d value are under threat from the attackers. Any auction protocol must not leak the anonymity and the privacy of the b i d value of an honest Bidder. Keeping these requirements in mind, we have firstly proposed a controlled traceable blind signature scheme (CTBSS) because e-auction schemes should be able to trace the Bidders. Using CTBSS, a blind sealed-bid electronic auction scheme is proposed (BSEA). We have incorporated the notion of blind signature to e-auction schemes. Moreover, both the schemes are based upon elliptic curve cryptography (ECC), which provides a similar level of security with a comparatively smaller key size than the discrete logarithm problem (DLP) based e-auction protocols. The analysis shows that BSEA fulfills all the requirements of e-auction protocol, and the total computation overhead is lower than the existing schemes.

Blind signatures using light variations in CCD sensors as a pattern to avoid identity forging

The implementation of countermeasures to avoid licence abuse is now obligatory, especially with the burgeoning of the Internet. The protocol proposed here is implemented within the session initiation protocol (SIP); this has been selected as the official end‐to‐end signalling protocol for establishing multimedia sessions in the Universal Mobile Telecommunication Systems network. This paper introduces blind signatures, enforced with user‐specific and unique data, modelled from CCD sensors to trace users of these online services, thus avoiding licence sharing that gives access to them. Blind signatures are useful in providing anonymity and establishing a way to tag users. The proposed protocol takes advantage of elliptic curve‐based cryptosystems – smaller key sizes and lower computational resources, an interesting issue for session establishment in S‐Universal Mobile Telecommunication Systems (satellite‐linked networks), where fast and light authentication protocols are a requirement ideal. SIP is a powerful signalling protocol for transmitting media over Internet protocol. Authentication is a vital security requirement for SIP. Hitherto, many authentication schemes have been proposed to enhance SIP security; indeed, the problem of impersonation is one of the topics most discussed. Consequently, a novel authentication and key agreement scheme is proposed for SIP using an elliptic curve cryptosystem. Copyright © 2016 John Wiley & Sons, Ltd.

Elliptic‐curve cryptography for wireless sensor network nodes without hardware multiplier support

AbstractWith its relatively small key size, elliptic‐curve cryptography (ECC) is considered as the public‐key cryptographic algorithm of choice for wireless sensor networks (WSNs). In this work, we implemented ECC in the frequency domain, that is, by using the number theoretic transform, and without using hardware multiplier support, on the constrained MSP430 microcontroller widely used in WSNs. Our 169‐bit ECC implementation uses Edwards curves and performs scalar point multiplication in only 1.97 and 0.98 s for multiplication of random and fixed points, respectively. Unlike many implementations in literature, our implementation does not use hardware multiplier support, which makes it desirable for low‐power applications on constrained WSN platforms. To our knowledge, this study presents the first ever software implementation of ECC in the frequency domain on a constrained low‐power microcontroller without hardware multiplier support. Copyright © 2016 John Wiley & Sons, Ltd.

Cryptanalytic Attacks on IDEA Block Cipher

International data encryption algorithm (IDEA) is a secret key or symmetric key block cipher. The purpose of IDEA was to replace data encryption standard (DES) cipher, which became practically insecure due to its small key size of 56 bits and increase in computational power of systems. IDEA cipher mainly to provide data confidentiality in variety of applications such as commercial and financial application e.g. pretty good privacy (PGP) protocol. Till 2015, no successful linear or algebraic weaknesses IDEA of have been reported. In this paper, author explained IDEA cipher, its application in PGP and did a systematic survey of various attacks attempted on IDEA cipher. The best cryptanalysis result which applied to all keys could break IDEA up to 6 rounds out of 8.5 rounds of the full IDEA cipher1. But the attack requires 264 known plaintexts and 2126.8 operations for reduced round version. This attack is practically not feasible due to above mention mammoth data and time requirements. So IDEA cipher is still completely secure for practical usage. PGP v2.0 uses IDEA cipher in place of BassOmatic which was found to be insecure for providing data confidentiality.

Elliptic Curve Cryptography-Based RFID Authentication Resisting Active Tracking

The challenge of authentication for radio frequency identification (RFID) with low computing capacities call for computation-efficient authentication that can achieve mutual authentication, anonymity, and tracking resistance. The excellent performance of elliptic curve cryptography (ECC) including its strong security, its small key size and efficient computation has attracted many researchers' attention in designing RFID authentication. Recently there are several promising ECC-based RFID authentication schemes aimed at achieving the above functions. Despite of their good performance in terms of computation and general security properties, we find that they all fall in the same security pitfall-being vulnerable to active tracking. In this paper, we identify these weaknesses and then propose a new ECC-based RFID authentication which conquers the weakness and even improves the computational performance.

A Study of Hyperelliptic Curves in Cryptography

Elliptic curves are some specific type of curves known as hyper elliptic curves. Compared to the integer factorization problem(IFP) based systems, using elliptic curve based cryptography will significantly decrease key size of the encryption. Therefore, application of this type of cryptography in systems that need high security and smaller key size has found great attention. Hyperelliptic curves help to make key length shorter. Many investigations are done with regard to improving computations, hardware and software implementation of these curves, their security and resistance against attacks. This paper studies and analyzes researches done about security and efficiency of hyperelliptic curves.

Pseudonym Creation and Parameter Based Key Generation for a Robust Authentication using ECC

Security is an important aspect in every field today and it cannot be neglected whatsoever. Network security has become one of the most important concerns of this generation due to its wide range of applications. With the emerging techniques in elliptic curve cryptography (ECC), it has now become the mainframe of many cryptosystems. Due to the generation of small key sizes in ECC, it poses as a favourable cryptosystem that can be used to minimize memory consumption. The previous schemes that were developed were unable to achieve user anonymity and were also vulnerable to stolen-verifier attacks, offline password guessing and insider attacks. The proposed scheme aims at improving the security provided to a user during authentication phase involved in any transaction. A step-by-step process is outlined in order to enhance security. It intends to provide a system involving Elliptic curve cryptography along with One Time Passwords to implement a new authentication scheme that overcomes certain threats to network security. The main features of this scheme includes generation of a common key with scalar multiplication, provision of user anonymity in order to prevent man-in-the-middle attacks using the Elliptic curve base point and a random number in order to prevent session hijacking attack or replay attack. This authentication paradigm finds its applications in ATM systems, RFID tags, smart card applications, mobile applications with SIM cards and so on. The proposed scheme works favourably with devices that have less resources (like memory).

Integration of Elliptical Cryptography with RSA and Steganography using Biometric Authentication

Cryptography is a science of encrypting data to make it non readable and secure. But with time traditional cryptography is not that reliable because of multiple types of attacks on it. So, to make it effective it can be integrated with latest techniques available. Here in this paper a new mechanism has been proposed which integrates RSA and steganography with elliptical cryptographic technique along with biometric authentication as an addition security measure. This method provides good security with small key size too.