Hashing into jacobi quartic curves
WebSearch ACM Digital Library. Search Search. Advanced Search WebAbstract. This article proposes four optimizations of indi erentiable hashing onto (prime order subgroups of) ordinary elliptic curves over nite elds F q. One of them is dedicated to elliptic curves Eprovided that q 2 (mod 3). The second deals with q 2;4 (mod 7) and an elliptic curve E 7 of j-invariant 3 35 . The corresponding section plays a ...
Hashing into jacobi quartic curves
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WebHashing into Jacobi Quartic Curves Wei Yu 1,2(B), Kunpeng Wang ,BaoLi, Xiaoyang He , and Song Tian1 1 Institute of Information Engineering, Chinese Academy of Sciences, Beijing 10 WebSo to add some items inside the hash table, we need to have a hash function using the hash index of the given keys, and this has to be calculated using the hash function as …
WebWe describe a hashing function from the elements of the finite field \(\mathbb{F}_q\) into points on a Hessian curve. Our function features the uniform and smaller size for the … Web14. The method explained in Husemöller's book on elliptic curves is as follows: Take a general quartic v 2 = f 4 ( u) = a o u 4 + a 1 u 3 + a 2 u 2 + a 3 u + a 4, and let. u = a x + b c x + d v = a d − b c ( c x + d) 2 y. Substituting you get:
WebSep 9, 2015 · With these two deterministic encodings, two hash functions from messages directly into Jacobi quartic curves are constructed. … WebJan 1, 2010 · Such a hash function can be plugged into any cryptosystem that requires hashing into elliptic curves, while not compromising proofs of security in the random …
WebAn elliptic curve in Jacobi quartic form can be obtained from the curve E a,b in the Weierstrass form with at least one point of order 2. The following transformation f sends …
WebWhen hashing into the Jacobian of an (hyper)elliptic curve, we need a func-tion that maps in a deterministic way an element of a finite field F q to a point of the curve. Such … bolt bluetooth instructionsWebFeb 4, 2024 · Hashing into elliptic curves is a key step in a myriad of cryptographic protocols and schemes. The password authenticated key exchange protocols [] and simple password exponential key exchange [] protocols are examples of the utilization of such hashing algorithms.Moreover, identity-based schemes like Lindell’s universally … boltbody isacWeb2. THE JACOBI QUARTIC One model for elliptic curves is known as Jacobi quartics. a background on these curves, see [3], [4], [17]. We recall only the basic facts. For the remainder of this paper, let K be a field whose characteristic is not 2 or 3. Any elliptic curve with a point of order 2 can be put into Jacobi quartic form, with equation. J gmail steam email verificationWebThis work derived maps for elliptic curves represented in Jacobi Intersection and Twisted Hessian models by following a multiplicative strategy that contrasts with the additive idea presented in the Velu formula. The security of public-key systems is based on the difficulty of solving certain mathematical problems. With the possible emergence of large-scale … gmail stony brook logingmail stationery backgroundJacobi quartic curves , one type of elliptic curves, are widely used for efficient arithmetics and immunity to timing attacks. The order of group of rational points on Jacobi quartic curves is divisible by 2 [24, 25]. Jacobi quartic curves can provide a larger group than Huff elliptic curves, Montgomery-form elliptic … See more We construct the deterministic encoding from \mathbb {F}_q to g(s)=s(s^2-4as+4a^2-4d). g(s) is an intermediate variable for the convenience of constructing … See more (Character Sum). Suppose f is an encoding from \mathbb {F}_q into an elliptic curve E, and J(\mathbb {F}_q) denotes the Jacobian group of E, \chi is a character of J(\mathbb {F}_q). We define the character sum … See more Note that the value of r is not required to be known in computing X_2, X_3 and U; indeed, these only depend on g(r). For this reason, r does not have to be explicitly computed and we … See more (Corollary 2, [30]). If f: \mathbb {F}_q\rightarrow E(\mathbb {F}_q) is a B-well-distributed encoding into a curve E, then the statistical distance between the distribution defined by f^{\otimes s} on J(\mathbb {F}_q)and … See more gmail stationary templateWeband Hashing into Elliptic and Hyperelliptic Curves. Pages615—648. 1. Introduction When hashing into the Jacobian of an (hyper)elliptic curve, we need a func-tion that maps in a deterministic way an element of a finite field F q to a point of the curve. Such function is called an encoding . We need encoding bolt board