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### How to Hash into Elliptic Curves [chapter]

Thomas Icart
2009 Lecture Notes in Computer Science
The function requires to compute a cube root. As an application we show how to hash deterministically into an elliptic curve.  ...  We describe a new explicit function that given an elliptic curve E defined over Fpn, maps elements of Fpn into E in deterministic polynomial time and in a constant number of operations over Fpn .  ...  I wish to thank Jean-Sébastien Coron for the time he spent to help me write this paper.  ...

### Efficient Indifferentiable Hashing into Ordinary Elliptic Curves [chapter]

Eric Brier, Jean-Sébastien Coron, Thomas Icart, David Madore, Hugues Randriam, Mehdi Tibouchi
2010 Lecture Notes in Computer Science
While almost as efficient as Icart's encoding, this hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random  ...  For hashing into an ordinary elliptic curve, the classical approach is inherently probabilistic: one can first compute an integer hash value x = h(m) and then determine whether x is the abscissa of a ⋆  ...  Acknowledgments We would like to thank Pierre-Alain Fouque and the anonymous referees of Eurocrypt 2010 and Crypto 2010 for useful comments on this paper.  ...

### Probability Distributions for Elliptic Curves in the CGL Hash Function [article]

Dhruv Bhatia, Kara Fagerstrom, Maximillian Watson
2021 arXiv   pre-print
We are interested in the elliptic curve CGL hash function, which maps a bitstring to an elliptic curve by traversing an input-determined path through an isogeny graph.  ...  The nodes of an isogeny graph are elliptic curves, and the edges are special maps betwixt elliptic curves called isogenies.  ...  To evaluate its security, we analyze how difficult the CGL hash function is to predict.  ...

### DEFEATING MITM ATTACKS ON CRYPTOCURRENCY EXCHANGE ACCOUNTS WITH INDIVIDUAL USER KEYS

Cheman Shaik
2021 Zenodo
Described in detail is as to how aman-in-the-middle attack takes place and how the proposed scheme defeats the attack.  ...  In this scheme, a separate public and private key pair is assigned to every account and the public key is shifted either forward or backward on the elliptic curve by a difference of the account user's  ...  point on the elliptic curve.  ...

### Deterministic Encoding and Hashing to Odd Hyperelliptic Curves [chapter]

Pierre-Alain Fouque, Mehdi Tibouchi
2010 Lecture Notes in Computer Science
The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux's supersingular elliptic curves.  ...  This makes it easy to construct well-behaved hash functions to the Jacobian J of H, as well as injective maps to J(Fq) which can be used to encode scalars for such applications as ElGamal encryption.  ...  We are grateful to Reza Farashahi and anonymous referees for useful comments, and to Masayuki Abe, Jean-Sébastien Coron and Thomas Icart for earlier discussions that inspired this paper.  ...

### Cryptography Based Secured Lifi For Patient Privacy And Emergency Health Care Service

A.K. Swedha, R. Sujatha
2017 International Journal of MC Square Scientific Research
As a solution for this problem, the model proposed here uses Elliptic Curve Diffie Hellman and Secure Hash Algorithms to provide utmost security.  ...  Elliptic Curve Diffie Hellman is used as an asymmetric function that is, it uses two keys which in turn makes it difficult to hack.  ...  The algorithm used is Elliptic Curve Diffie-Hellman. Elliptical Curve Diffie-Hellman Algorithm: Elliptical Curve Diffie-Hellman is one of the public-key cryptosystem.  ...

### Performance Evaluation of Android Pattern Authentication Systems

Robert Wang, Stephan Chan, Yung-Cheng Chang
2019 Zenodo
Therefore this research presents an alternative representation for mobile patterns using elliptic curves, and proposes three algorithms based on this ideology to make the pattern passwords strong against  ...  Android Kit Kat and Lollipop pattern authentication systems are vulnerable to pre-computations since they use SHA-1 unsalted hashes.  ...  The security and efficiency of elliptic curve based protocols such as encryption, signature generation, authentication, secret key exchange etc. depends on how tough it is to resolve the discrete logarithm  ...

### Analysis of possibility to use El Gamal algorithm with deterministic embedding for key encapsulation

O.V. Tsygankova
To use this algorithm on elliptic curve, we need algorithms for embedding key into point on elliptic curve and for retrieving it back.  ...  To solve the problem of embedding key into point on elliptic curve and retrieving it, Koblitz in [9] proposed some probabilistic algorithm of embedding k into elliptic curve point.  ...  We use the equalities (3) and (4) Conclusion We described deterministic algorithms for key embedding into elliptic curve point and for key retrieving.  ...

### Secure and Efficient Authentication Scheme for Cloud Computing

Mohamed M., Ahmed A., Ahmed H.
2016 International Journal of Computer Applications
In this paper; an efficient and provably secure authentication mechanism is proposed to give a legitimate user the right to access and manage the cloud resources.  ...  It provides a convenient on demand network access to a pool of shared services and resources via public networks.  ...  The following sections will introduce elliptic curve concepts and how it is used in cryptography to provide an efficient and reliable way to control the access to the cloud services and resources.  ...

### Elliptic Curve Multiset Hash [article]

Jeremy Maitin-Shepard, Mehdi Tibouchi, Diego Aranha
2016 arXiv   pre-print
In this paper, we introduce the Elliptic Curve Multiset Hash (ECMH), which combines a usual bit string-valued hash function like BLAKE2 with an efficient encoding into binary elliptic curves to overcome  ...  Unfortunately, constructions of homomorphic hash functions in the literature are hampered by two main drawbacks: they tend to be much longer than usual hash functions at the same security level (e.g. to  ...  For elements longer than b bits, this is likely to be significantly more expensive than hashing a with a fast hash function like BLAKE2 and then encoding the result into a single elliptic curve point.  ...

### Analysis of the Cryptographic Tools for Blockchain and Bitcoin

Víctor Gayoso Gayoso Martínez, Luis Hernández-Álvarez, Luis Hernández Hernández Encinas
2020 Mathematics
Among other elements, hash functions, digital signatures, elliptic curves, and Merkle trees are reviewed in the scope of their usage as building blocks of this technology.  ...  Blockchain is one of the most interesting emerging technologies nowadays, with applications ranging from cryptocurrencies to smart contracts.  ...  Elliptic Curves In this section, the reader is presented with the mathematical description of elliptic curves, so it is possible to completely understand how the elliptic curve signature algorithm employed  ...

### Achieving Authentication and Integrity using Elliptic Curve Cryptography Architecture

2013 International Journal of Computer Applications
The parameters to considered choosing Elliptic Curves are presented in NIST document of recommended elliptic curves.  ...  on the arithmetic of elliptic curves and discrete logarithmic problems.  ...  Introduction to Elliptic Curve Cryptosystems Elliptic curves have been used to solve a range of problems by mathematicians.  ...

### A Novel Approach to Thwart Security Attacks on Mobile Pattern Authentication Systems

2018 International Journal of Computer Network and Information Security
) value for SHA-1 hashes to avoid such attacks without using an added hardware, for mobile computers using elliptic curves.  ...  To avoid such a security breaches on pattern passwords, many methodologies have been proposed so far such as an elliptic curve based salt generation techniques.  ...  We proposed a modified approach to generate the salt and pepper for SHA-1 hashes based on elliptic curves [25] .  ...

### Secured Data Storage Using Deduplication in Cloud Computing Based on Elliptic Curve Cryptography

N. Niyaz Ahamed, N. Duraipandian
2022 Computer systems science and engineering
So, we suggest a model called multi-layer storage (MLS) based on security using elliptical curve cryptography (ECC).  ...  Based on divide and combine methodologies, the data are divided into three parts.  ...  It measures the hops needed to travel from one point on an elliptic curve to another. Elliptic curves are symmetrical over the x-axis and are binary curves.  ...

### Efficient Data Security for Mobile Instant Messenger

Putra Wanda, Huang J. Jie
2018 TELKOMNIKA (Telecommunication Computing Electronics and Control)
In this research, security method proposes new algorithms based on Elliptic Curve (EC) works in Peer to Peer (P2P) architecture than a conventional client-server model.  ...  This paper proposes a new efficient method for securing message both in encryption and authentication within the end-to-end model.  ...  In this research, secure module applied the hash algorithm. The main function of the hash algorithm is to convert into a hash value.  ...
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