To reduce bandwidth in elliptic curve cryptography one can transmit only x-coordinates of points (or x-coordinates together with an extra bit). This is called point compression. For further computation using the points one can either recover the y-coordinates by taking square roots or one can use point multiplication formulae which use x-coordinates only. We consider how to efficiently use point compression in pairing-based cryptography when the embedding degree is even. We give a method to compute compressed pairings using x-coordinates only. We also show how to compute the compressed pairings using two x-coordinates and one y-coordinate. Our methods are more efficient than taking square roots when the embedding degree is small. We implemented the algorithms in the case of embedding degree 2 curves over mathbb Fp{mathbb {F}_p} where p º 3{p equiv 3} (mod 4) and found that our methods can be 10–15% faster than the analogous methods using square roots.
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机译：为了减少椭圆曲线密码术的带宽，人们只能传输点的x坐标（或x坐标和一个额外的位）。这称为点压缩。为了进一步利用这些点进行计算，可以通过取平方根来恢复y坐标，也可以使用仅使用x坐标的点乘法公式。我们考虑当嵌入度为偶数时如何在基于配对的密码学中有效使用点压缩。我们提供了一种仅使用x坐标来计算压缩配对的方法。我们还将展示如何使用两个x坐标和一个y坐标来计算压缩配对。当嵌入程度较小时，我们的方法比取平方根更有效。我们在mathbb F p {mathbb {F} _p}上嵌入2度曲线的情况下实现了算法，其中pº3 {p equiv 3}（mod 4），发现我们的方法可以比使用平方根的类似方法快10–15％。
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