# hyper-elliptic curve

## Top PDF hyper-elliptic curve:

### An Hyper-Elliptic Curve Cryptosystem Scheme Using 3bc Algorithm

Is a polynomial of degree not larger than g and f(x) โ K[x] is a monic polynomial of degree 2g + 1 [7]. From this definition it follows that elliptic curves are hyper-elliptic curves of genus 1. In hyper-elliptic curve cryptography K is often a finite field. The Jacobian of C, denoted J(C), is a quotient group, thus the elements of the Jacobian are not points, they are equivalence classes of divisors of degree 0 under the relation of linear equivalence. This agrees with the elliptic curve case, because it can be shown that the Jacobian of an elliptic curve is isomorphic with the group of points on the elliptic curve. The use of hyper-elliptic curves in cryptography came about in 1989 from Neal Koblitz [14]. Although introduced only 3 years after ECC, not many cryptosystems implement hyper-elliptic curves because the implementation of the arithmetic isn't as efficient as with cryptosystems based on elliptic curves or factoring (RSA). The efficiency of implementing the arithmetic depends on the underlying finite field K, in practice it turns out that finite field of characteristic 2 are good choices for hardware implementations while software is usually faster in odd characteristic.

### An Efficient Encryption Schemes based on Hyper-Elliptic Curve Cryptosystem

Some researcherโs interests have recently fall on Hyper- Elliptic Curve because it offers equal security for a smaller key size. Since, HECC is a typically fast public key cryptosystem and it has superiority and more application efficiency. There are some superiorities of Hyper-Elliptic Curve cryptosystem such as high efficiency, short key length as compared with other public key cryptosystems and they are as follows:

### Efficient Computation For Hyper Elliptic Curve Based Cryptography

In this thesis we have proposed explicit formulae for group operation such as addition and doubling on the Jacobians of Hyper Elliptic Curves genus 2, 3 and 4. The Cantor Algorithm generally involves to perform arithmetic operations in the polynomial ring . The explicit method performs the arithmetic operation in the integer ring of . Significant improvement has been made in the explicit formulae algorithm proposed here. Other explicit formulae used Montgomery trick to derive efficient formulae for faster group computation. The method used in this thesis to develop an efficient explicit formula was inspired by the geometric properties in the hyper elliptic curves of genus and by keeping the Jacobian variety curve constant. This formulae take Mumford coordinates as input. The explicit formulae here performs the computation in affine space of genus 2, 3 and 4 of Hyper Elliptic Curves in general form, which can be used to develop Hyper Elliptic Curve Cryptosystem.

### Key Generation in Elliptic Curve Cryptosystems over GF(2 n

In the study of cryptosystem, hyper-elliptic curve has recently attracted some researchersโ interests because it gives The main attraction of combining EC with HEC is that it appears to offer equal security for a far smaller key size, thereby saving the processing overhead because it gives the same security level with a smaller key length as compared to cryptosystems using elliptic curves. From the fact it is expected to be possible to use hyper-elliptic curves to factor integers, since elliptic curve method exploits the property of the Abelian groups in the same way as the cryptosystems.

### A SURVEY ON DATA ENCRYPTION USING DNA TECHNIQUE

In [24], authors have presented a paper on enhanced level of security using DNA computing technique with hyper elliptic curve cryptography. DNA based elliptic curve cryptographic technique require larger key size to encrypt and decrypt the message resulting in increased processing time, more computational and memory overhead. To overcome the above limitations, DNA strands are used to encode the data to provide first level of security and HECC encryption algorithm is used for providing second level of security. HECC is better than the existing public key cryptography technique such as RSA, DSA, AES and ECC in terms of smaller key size. DNA cryptography is a next generation security mechanism, storing almost a million gigabytes of data inside DNA strands. Hence this proposed integration of DNA computing based HECC provides higher level of security with less key size of HECC-80 bits than ECC-160 bits and with less computational and memory overhead.

### Proxy Signcrypion Scheme Based on Hyper Elliptic Curves

Gamage extended the concept of proxy signature and proposed a new cryptography primitive called proxy signcrypion [3]. Proxy signcrypion scheme allows the original user (Alice) to transfer the signing capability to the trusted entity known as proxy signcrypter. The proxy signer signcrypt the message on behalf of the original user and sends to the recipient (Bob) . Proxy Signcrypion schemes based on discrete logarithm problem (DLP) and elliptic curve discrete logarithm problem (ECDLP) were proposed. The common problems of these schemes are high computational cost and more communication overhead. In this paper, proxy signcrypion based on hyper elliptic curve is proposed, whose security relies on the hardness of the hyper elliptic curve discrete logarithm problem (HECDLP). In order to achieve the same security level, NIST has recommended key length of 80 bits for HECC, 1024 bits for RSA and 160 bits for ECC. Hyper elliptic curve is of public key cryptosystem with small key length. The proposed scheme saves the computational and communication cost due to its shorter key size. The scheme achieves the security properties.

### Cloud Computing Security Framework based on Elliptical Curve

The signature will be the pair (x, y) The signature is used to authenticate between application components so that data transmitted only to known parties. For Securing API and Interfaces, the shared secret key used to ensure strong authentication and access controls with encrypted transmission. The client can access the cloud by applying their shared secret key, which is monitor by the cloud environment. They can demand the cloud environment according to their choice and need. The signed message encrypted using ElGamal cryptosystem based on elliptic curve. The client selects a private integer named ๐ข๐ ๐๐ ๐๐๐๐ฃ . This private number used to generate a public key name ๐ข๐ ๐๐ ๐๐ข๐ for encryption process. This public key represents a point on the curve. The encryption based on Elgamal algorithm generates two points on the curve named point c1 and point c2. ๐๐๐๐๐ก ๐1 = ๐ข๐ ๐๐ ๐๐๐๐ฃ โ ๐ ๐๐๐ฆ (๐๐๐ ๐) (7)

### Data and Information Security in Modern World by using Elliptic Curve Cryptography

From table (2a), figure (2a) and (2b) we can see that bit size does not affect our algorithms encryption and decryption time. Comparison As our proposed of algorithm requires mapping, we compared our algorithm with those algorithm which requires mapping. Implementation of Elliptic Curve Cryptography on Text and Image [7] and Implementation of Text based Cryptosystem using Elliptic Curve Cryptography [6] simulation was performed using Lenovo ideapad Z510 laptop with system configuration of i7 processor @2.20GHz and 8GB Ram [6]. Our simulation is done by using Toshiba Satellite C600 with system configuration dual core processor @2.30 GHz and 2 GB Ram. Word length=409, Text Length: 2325. We have done our comparison with only those methods where mapping is required.

### Hyper-and-elliptic-curve cryptography

a speedup factor around 3, depending on various details of field arithmetic. The disadvantage of genus 2 is that each group operation requires many more field operations; but for Gaudryโs [24] Kummer-surface formulas this loss factor is only slightly above 2. Even better, 24% of Gaudryโs field multiplications are multiplications by curve parameters that can be chosen to be small; a secure small-parameter genus-2 curve was announced by Gaudry and Schost [27] after a massive point-counting computation. A further advantage of genus 2, exploited in a very recent paper [4] by Bernstein, Chuengsatiansup, Lange, and Schwabe, is a synergy between the structure of Gaudryโs formulas and the availability of vector operations in modern CPUs. One can speed up genus 1 using โnon-constant-timeโ addition chains. However, non-constant- time computations are a security problem; see, e.g., the attacks cited in [4, Section 1.2].

### ABSTRACT : In this paper we purposed an image based cryptography that Elliptic Curve cryptography (ECC)

In the paper we have presented the implementation technique of image encryption/decryption and inclusion of digital signature to the cipher image to provide authenticity and integrity to the received image. We have performed our operation by grouping the pixel and explained how many pixels can be grouped according to the ECC parameters. Pairing of the grouped pixel value was performed instead of mapping those values to Elliptic curve coordinate. It helps to ignore the used of reference mapping table for encryption and decryption. Our algorithm generates a low correlated cipher image even with a image which is made up of same pixel value. We have also analysed our technique to support the strength of the algorithm.

### Security Authentication through a Near-Field Communication in Asymmetric Cryptography

This paper presents the design and implementation of a complete near-field communication (NFC) tag system that supports high-security features. The tag design contains all hardware modules required for a practical realization, which are: an analog 13.56-MHz radio-frequency identification (RFID) front-end, a digital part that includes a tiny (programmable) 8-b microcontroller, a framing logic for data transmission, a memory unit, and a crypto unit. All components have been highly optimized to meet the fierce requirements of passively powered RFID devices while providing a high level of flexibility and security. The tag is fully compliant with the NFC Forum Type-4 specification and supports the ISO/IEC 14443A (layer 1โ4) communication protocol as well as block transmission according to ISO/IEC 7816. Its security features include support of encryption and decryption using the Advanced Encryption Standard (AES- 128), the generation of digital signatures using the elliptic curve digital signature algorithm according to NIST P-192, and several countermeasures against common implementation attacks, such as side-channel attacks and fault analyses. The chip has been fabricated in a 0.35-ฮผm CMOS process technology, and requires 49 999 GEs of chip area in total (including digital parts and analog front-end).

### Hardware Accelerators for Elliptic Curve Cryptography

Data security is an important requirement for many appli- cations in our daily life. Especially internet applications such as e-commerce need to transmit secret data via inse- cure communication channels. Therefore, various crypto- graphical methods exist that allow to protect sensitive data. Asymmetric cryptography, which is also known as public- key cryptography, does not only provide algorithms for en- cryption and decryption of data, but also for digital signa- tures and authentication. Recently asymmetric cryptography based on elliptic curves is gaining interest. Compared to traditional asymmetric techniques, e.g. the RSA algorithm, the elliptic curve cryptography (ECC) achieves an equivalent level of security with smaller key sizes. Using elliptic curve cryptography therefore results in memory as well as band- width savings.

### EFFICIENT MAPPING METHODS FOR ELLIPTIC CURVE CRYPTOSYSTEMS

Suppose that we had a way of masking the contents of messages or other information traffic so that an attacker, even if he or she captured the message, would be unable to extract the information from the message. The common technique for doing masking is encryption. The encryption is done by using Symmetric key or public key Algorithms. The most commonly used public key algorithms are 1. Rivest Shamir Adelman(RSA) and 2 Elliptic Curve cryptography

### Ed3363 (HighFive) -- An alternative Elliptic Curve

However we had another criteria in mind which was to exploit the Granger-Scott idea [5] for fast modular arithmetic. This guided our choice of the modulus p. We also wanted a curve that would be implemented just as conveniently on both 32-bit and 64-bit architectures. Whereas a nice fit to a 64-bit architecture facilitates record-setting, in our view a good fit to a 32-bit architecture is probably more important in practise. As a bonus we wanted our implementation to be e๏ฌcient even when written in a portable high-level language.

### Ed448-Goldilocks, a new elliptic curve

When designing Goldilocks, I hypothesized that timings within the same implementation strat- egy should roughly follow a power law t โ b k , where b is the bits in the field size and k is some exponent, and therefore that b k /t might be described as an โefficiency scoreโ. I evaluated designs with Karatsubaโs k = 1 + log 3/ log 2, which works surprisingly well even though not all the designs use Karatsuba multiplication. In arbitrary units 2 , Ed448-Goldilocks and E-521 score 3.3 and 3.1 by this metric. ECCLibโs ed-384-mers and ed-512-mers both score 2.3, and the optimized secp256r1 scores 1.4. By this metric, Goldilocks is about 40% more efficient than either ed-mers curve on Haswell.

### An Efficient Protocol for Securing Multiple Patient&apos;s Privacy in Wireless Body Sensor Network using ECIES

This algorithm can be applied to achieve multiple reading simultaneously at the same time and by using the identity of a particular patient the reading can be accessed. To setup ECC, we first select a particular elliptic curve E over GF (K), where k is a big prime number. We also denote G as the base point of E and q as the order of K, where q is also a big prime. We then pick a secret key x, and the corresponding public key y, where y = x ยทG, and a Message Authentication Code hash function. Finally, we have the secret key x and public parameters (Y, K, k, q, h (.) G). Encrypting a message m using public key Y as EciesEncrypt (m, Y). The Elliptic curve integrated encryption standard technique consists of reading the data from the sensors which is then encrypted in the sensors using Algorithm 1.The Algorithm 2 is used to decrypt the data. The Algorithm 3 is used to encrypt the data using a public key i.e. the identity of the patient. The Algorithm 4 is used by the doctor to decrypt the data using the identity of the patient. The Algorithm 6 is used to provide a certificate for both the identity of the patient and the doctor so that the identities of both are stored as PKG in the storage site which is then used to verify the doctor and decrypt the reading. The resulting ciphertext is denoted by c. The decryption of ciphertext c using the secret key x is given as EciesDecrypt(c, x). The recipient is assumed to have a long-term public /private key pair (Y, x) where

### Survey on network security using cryptography by Both decryption encryptions

Elliptic curve arithmetic can be used to develop a variety of elliptic curve cryptography (ECC) schemes, including key exchange, encryption, and digital signature. For pur[r]

### Survey of Elliptic Curve Scalar Multiplication Algorithms

Elliptic curve based protocols such as Elliptic Curve Diffie-Hellman (ECDH), Elliptic Curve Digital Signature Algorithm (ECDSA) and Elliptic Curve Integrated Encryption Scheme (ECIES) involves scalar multiplications. The speed of scalar multiplication plays a vital role in deciding the efficiency of the whole system. In particular, fast multiplication is more crucial in some environments such as e-commerce servers where the large number of key agreements or signature generations occurs, and handheld devices with low computational power. There has been extensive research to compute scalar multiplication efficiently based on various representations of the multiplier [7].