In this paper, we introduce Bandersnatch, a new elliptic curve built over the BLS12-381 scalar field. The curve is equipped with an efficient endomorphism, allowing a fast scalar multiplication algorithm. Our benchmark shows that the multiplication is 42% faster, 21% reduction in terms of circuit size in the form of rank 1 constraint systems (R1CS), and 10% reduction in terms of Plonk circuit, compared to another curve, called Jubjub, having similar properties. Many zero-knowledge proof systems that rely on the Jubjub curve can benefit from our result.

中文翻译：

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Bandersnatch：在 BLS12-381 标量场上构建的快速椭圆曲线

在本文中，我们介绍了 Bandersnatch，这是一种在 BLS12-381 标量场上构建的新椭圆曲线。该曲线配备了高效的自同态，允许快速标量乘法算法。我们的基准测试表明，与另一条称为 Jubjub 的曲线相比，乘法速度快了 42%，以 1 级约束系统 (R1CS) 形式表示的电路尺寸减少了 21%，Plonk 电路减少了 10%，类似的属性。许多依赖 Jubjub 曲线的零知识证明系统可以从我们的结果中受益。