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Uniform encodings to elliptic curves and indistinguishable point representation

机译：椭圆曲线的均匀编码和无法区分的点表示

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Many cryptographic protocols which are based on elliptic curves require to efficiently encode bit-strings into the points of a given elliptic curve such that the encoding function satisfies computability, regularity, and samplability, or generally admissibility. All the admissible encoding functions from the finite field Fq are restricted to the class of elliptic curves with a non-trivial l-torsion Fq-rational point, where l is an element of{2,3}. Therefore, there is no admissible encoding function to the class of many cryptographically interesting elliptic curves of prime order. In this paper, we present an admissible 2:1 encoding function from the set {0,1, horizontal ellipsis ,q-12} to the Fq-rational points of arbitrary elliptic curves. We also propose an injective encoding function to elliptic curves with a non-trivial Fq-rational point of order two, that acts the same as the Bernstein et al.'s injective encoding function. Conversely, occasionally we have to transmit points of a known curve through an insecure channel. Traditional methods for transferring points enable an adversary to recognize patterns in the transmitted data. Consequently, one finds valuable information to attack the cryptosystem using the network traffic. By the help of the inverse of the injective encoding functions, Bernstein et al. introduced an interesting solution to this problem, namely Elligator. In this paper, we present an indistinguishable elliptic curve point representation using our given encoding function, which unlike the previous well-known encoding functions is not injective but covers almost all of elliptic curves over odd characteristic finite fields. Indeed, since we proposed a 2:1 encoding function to elliptic curves in short Weierstrass form, we have to select one pre-image randomly and transmit its corresponding bit-string instead of the point.
机译：基于椭圆曲线的许多加密协议需要有效地编码位字符串到给定的椭圆曲线的点，使得编码功能满足可计算性，规则性和可分配性，或通常可否受理。来自有限字段FQ的所有可接受的编码功能都仅限于具有非平凡的L-TOLESION FQ-Rational Point的椭圆曲线类，其中L是{2,3}的元素。因此，许多Prime订单的许多密码有趣的椭圆曲线类别没有可接受的编码功能。在本文中，我们提出了一个可允许的2：1编码功能，从集合{0,1，水平省略省略Q-12}到任意椭圆曲线的FQ合理点。我们还向椭圆形曲线提出了一种具有非平凡的FQ合理点的椭圆曲线，其用与Bernstein等人相同。的注射编码功能。相反，偶尔我们必须通过不安全的信道传输已知曲线的点。传输点的传统方法使逆境能够识别传输数据中的模式。因此，人们使用网络流量发现有价值的信息来攻击密码系统。通过反向注射编码功能的反向，Bernstein等人。向这个问题引入了一个有趣的解决方案，即闪光灯。在本文中，我们使用我们的给定编码函数呈现了一个无法区分的椭圆曲线点表示，这与先前的众所周知的编码功能不同，而不是注射函数，而是覆盖几乎所有椭圆曲线上的奇数特性有限场。实际上，由于我们提出了2：1编码函数到椭圆形曲线的短段形式，我们必须随机选择一个预图像并传输其对应的位串而不是点。

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