Remote sensing image encryption algorithm based on novel hyperchaos and an elliptic curve cryptosystem

Remote sensing images carry crucial ground information,often involving the spatial distribution and spatiotemporal changes of surface elements.To safeguard this sensitive data,image encryption technology is essential.In this paper,a novel Fibonacci sine exponential map is designed,the hyperchaotic performance of which is particularly suitable for image encryption algorithms.An encryption algorithm tailored for handling the multi-band attributes of remote sensing images is proposed.The algorithm combines a three-dimensional synchronized scrambled diffusion operation with chaos to efficiently encrypt multiple images.Moreover,the keys are processed using an elliptic curve cryptosystem,eliminating the need for an additional channel to transmit the keys,thus enhancing security.Experimental results and algorithm analysis demonstrate that the algorithm offers strong security and high efficiency,making it suitable for remote sensing image encryption tasks.

Sensitive Information Security Based on Elliptic Curves

The elliptic curve cryptography algorithm represents a major advancement in the field of computer security. This innovative algorithm uses elliptic curves to encrypt and secure data, providing an exceptional level of security while optimizing the efficiency of computer resources. This study focuses on how elliptic curves cryptography helps to protect sensitive data. Text is encrypted using the elliptic curve technique because it provides great security with a smaller key on devices with limited resources, such as mobile phones. The elliptic curves cryptography of this study is better than using a 256-bit RSA key. To achieve equivalent protection by using the elliptic curves cryptography, several Python libraries such as cryptography, pycryptodome, pyQt5, secp256k1, etc. were used. These technologies are used to develop a software based on elliptic curves. If built, the software helps to encrypt and decrypt data such as a text messages and it offers the authentication for the communication.

Verifiable (t, n) Threshold Signature Scheme Based on Elliptic Curve

Based on tht difficulty of solving the ECDLP (elliptic curve discretelogarithm problem) on the finite field, we present a (t, n) threshold signature scheme and averifiable key agreement scheme without trusted party. Applying a modified elliptic curve signatureequation, we gel a more efficient signature scheme than the existing ECDSA (elliptic curve digitalsignature algorithm) from the computability and security view. Our scheme has a shorter key, fastercomputation, and better security.

Binary Sequences from a Pair of Elliptic Curves

A family of binary sequences were constructed by using an elliptic curve and its twisted curves over finite fields. It was shown that these sequences possess ＂good＂ cryptographie properties of 0-1 distribution, long period and large linear complexity. The results indicate that such se quences provide strong potential applications in cryptography.

A New Digital Multilevel Proxy Signature Scheme Based on Elliptic Curve Cryptography

Based on the analysis of elliptic curve digital signature algorithm（ECDSA）,aiming at multilevel proxy signature in which the original signer delegates the digital signature authority to several proxies and its security demands, a new multilevel proxy signature scheme based on elliptic curve discrete logarithm problem （ECDLP） is presented and its security are proved.

Cryptography with Elliptic Curve Using Tifinagh Characters

The paper describes the concept of plaintext encryption by using the Unicode characters. In the case of elliptic curve cryptography, there is not specified rule or algorithm to specify the letters of Tifinagh as well as special characters. So, the paper gives the transformation of characters Tifinagh into points on elliptic curve by using the corresponding characters Latin. The obtained correspondence has been applied in Menezes-Vanstone cryptosystem based on elliptic curve. Therefore, the paper explains in detail its implementation in Maple 12.

Secure and efficient elliptic curve cryptography resists side-channel attacks

An embedded cryptosystem needs higher reconfiguration capability and security. After analyzing the newly emerging side-channel attacks on elliptic curve cryptosystem （ECC）, an efficient fractional width-w NAF （FWNAF） algorithm is proposed to secure ECC scalar multiplication from these attacks. This algorithm adopts the fractional window method and probabilistic SPA scheme to reconfigure the pre-computed table, and it allows designers to make a dynamic configuration on pre-computed table. And then, it is enhanced to resist SPA, DPA, RPA and ZPA attacks by using the random masking method. Compared with the WBRIP and EBRIP methods, our proposals has the lowest total computation cost and reduce the shake phenomenon due to sharp fluctuation on computation performance.

Addition Sequence Method of Scalar Multiplication of Elliptic Curve over OEF

A new elliptic curve scalar multiplication algorithm is proposed. Thealgorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence We introducea new algorithm on generating addition sequence efficiently and also give some analysis about it.Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over anOEF is presented. The new method is more efficient than the traditional scalar multiplicationalgorithms of elliptic curve over OEF. Thecomparisons of traditional method and the new method arealso given.

Integral Points on a Class of Elliptic Curve

We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory and p-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curve y^2= （x＋α）（x^2-α）（x^2-αx＋b） ,α ,b∈Z,α^2〈4b and find all integer solutions of hyperelliptic Diophantine equation Dy^2=Ax^4 ＋ Bx^2 ＋C,B^2〈4AC.

Cryptanalysis and Improvement of Signcryption Schemes on Elliptic Curves

In this paper, we analyze two signcryption schemes on elliptic curves proposed by Zheng Yu-liang and Hideki Imai. We point out a serious problem with the schemes that the elliptic curve based signcryption schemes lose confidentiality to gain non-repudiation. We also propose two improvement versions that not only overcome the security leak inherent in the schemes but also provide public verifiability or forward security. Our improvement versions require smaller computing cost than that required by signature-then-encryption methods.

RGB Based Multiple Share Creation in Visual Cryptography with Aid of Elliptic Curve Cryptography

In visual cryptography, many shares are generated which are illogical containing certain message within themselves. When all shares are piled jointly, they tend to expose the secret of the image. The notion of visual secret sharing scheme is to encrypt a secret image into n illogical share images. It is unable to reveal any data on the original image if at least one of the shares is not achieved. The original image, in fact, is realized by overlapping the entire shares directly, in order that the human visual system is competent to identify the collective secret image without employing any complicated computational tools. Therefore, they are communicated steadily as number of shares. The elliptic curve cryptography approach, in turn, is employed to augment the privacy and safety of the image. The new.fangled technique is utilized to generate the multiple shares which are subjected to encryption and decryption by means of the elliptic curve cryptography technique. The test outcomes have revealed the fact that the peak signal to noise ratio is 58.0025, Mean square error value is 0.1164 and the correlation coefficient is 1 for the decrypted image without any sort of distortion of the original image.

Efficient Dynamic Threshold Group Signature Scheme Based on Elliptic Curve Cryptosystem

The short secret key characteristic of elliptic curve cryptosystem （ECC） are integrated with the （ t, n ） threshold method to create a practical threshold group signature scheme characterized by simultaneous signing. The scheme not only meets the requirements of anonymity and traceability of group signature but also can withstand Tseng and Wang＇s conspiracy attack. It allows the group manager to add new members and delete old members according to actual application, while the system parameters have a little change. Cryptanalysis result shows that the scheme is efficient and secure.

Elliptic Curve Point Multiplication by Generalized Mersenne Numbers

Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.

Text Encryption Using Pell Sequence and Elliptic Curves with Provable Security

The demand for data security schemes has increased with the significant advancement in the field of computation and communication networks.We propose a novel three-step text encryption scheme that has provable security against computation attacks such as key attack and statistical attack.The proposed scheme is based on the Pell sequence and elliptic curves,where at the first step the plain text is diffused to get a meaningless plain text by applying a cyclic shift on the symbol set.In the second step,we hide the elements of the diffused plain text from the attackers.For this purpose,we use the Pell sequence,a weight function,and a binary sequence to encode each element of the diffused plain text into real numbers.The encoded diffused plain text is then confused by generating permutations over elliptic curves in the third step.We show that the proposed scheme has provable security against key sensitivity attack and statistical attacks.Furthermore,the proposed scheme is secure against key spacing attack,ciphertext only attack,and known-plaintext attack.Compared to some of the existing text encryption schemes,the proposed scheme is highly secure against modern cryptanalysis.

Elliptic Curve Scalar Multiplication with x-Coordinate

This paper gives a comprehensive method to do Elliptic Curve Scalar Multiplication with only x-coordinate. Explicit point operation formulae for all types of defining equations of the curves are derived. For each type of curve, the performance is analyzed. The formulae are applied in Montgomery Ladder to get scalar multiplication algorithm operated with only x-coordinate. The new scalar multiplication has the same security level and computation amount with protected binary scalar multiplication （PBSM） against side channel attack, and has the advantages of higher security and little memory needed.

An FPGA Implementation of GF(p) Elliptic Curve Cryptographic Coprocessor

A GF(p) elliptic curve cryptographic coprocessor is proposed and implemented on Field Programmable Gate Array (FPGA). The focus of the coprocessor is on the most critical, complicated and time-consuming point multiplications. The technique of coordinates conversion and fast multiplication algorithm of two large integers are utilized to avoid frequent inversions and to accelerate the field multiplications used in point multiplications. The characteristic of hardware parallelism is considered in the implementation of point multiplications. The coprocessor implemented on XILINX XC2V3000 computes a point multiplication for an arbitrary point on a curve defined over GF(2192?264?1) with the frequency of 10 MHz in 4.40 ms in the average case and 5.74 ms in the worst case. At the same circumstance, the coprocessor implemented on XILINX XC2V4000 takes 2.2 ms in the average case and 2.88 ms in the worst case.

A Heuristic Method of Scalar Multiplication of Elliptic Curve over OEF

Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given point. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over optimal extension field (OEF) using Frobenius map was presented. The new method is more efficient than the traditional ones. In the last part of this paper, the comparison was given in the end.

Design of Nonlinear Components Over a Mordell Elliptic Curve on Galois Fields

Elliptic curve cryptography ensures more safety and reliability than other public key cryptosystems of the same key size.In recent years,the use of elliptic curves in public-key cryptography has increased due to their complexity and reliability.Different kinds of substitution boxes are proposed to address the substitution process in the cryptosystems,including dynamical,static,and elliptic curve-based methods.Conventionally,elliptic curve-based S-boxes are based on prime field GF(p)but in this manuscript;we propose a new technique of generating S-boxes based on mordell elliptic curves over the Galois field GF(2n).This technique affords a higher number of possibilities to generate S-boxes,which helps to increase the security of the cryptosystem.The robustness of the proposed S-boxes against the well-known algebraic and statistical attacks is analyzed to classify its potential to generate confusion and achieve up to the mark results compared to the various schemes.The majority logic criterion results determine that the proposed S-boxes have up to the mark cryptographic strength.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

We propose a new fractional two-dimensional triangle function combination discrete chaotic map(2D-TFCDM)with the discrete fractional difference.Moreover,the chaos behaviors of the proposed map are observed and the bifurcation diagrams,the largest Lyapunov exponent plot,and the phase portraits are derived,respectively.Finally,with the secret keys generated by Menezes-Vanstone elliptic curve cryptosystem,we apply the discrete fractional map into color image encryption.After that,the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms.

AN IMPLEMENTATION OF FAST ALGORITHM FOR ELLIPTIC CURVE CRYPTOSYSTEM OVER GF(p)

The design and implementation of fast algorithms related to Elliptic Curve Cryptography (ECC) over the field GF(p), such as modular addition, modular subtraction, point addition, point production, choice of embedding plaintext to a point, etc. are given. A practical software library has been produced which supports variable length implementation of the ECCbased ElGamal cryptosystem. More importantly, this scalable architecture of the design enables the ECC being used in restricted platforms as well as high-end servers based on Intel Pentium CPU. Applications such as electronic commerce security, data encryption communication, etc.are thus made possible for real time and effective ECC.