# Module bls12_381::notes::serialization

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## BLS12-381 serialization

- $\mathbb{F}_p$ elements are encoded in big-endian form. They occupy 48 bytes in this form.
- $\mathbb{F}_{p^2}$ elements are encoded in big-endian form, meaning that the $\mathbb{F}_{p^2}$ element $c_0 + c_1 \cdot u$ is represented by the $\mathbb{F}_p$ element $c_1$ followed by the $\mathbb{F}_p$ element $c_0$. This means $\mathbb{F}_{p^2}$ elements occupy 96 bytes in this form.
- The group $\mathbb{G}_1$ uses $\mathbb{F}_p$ elements for coordinates. The group $\mathbb{G}_2$ uses $\mathbb{F}_{p^2}$ elements for coordinates.
- $\mathbb{G}_1$ and $\mathbb{G}_2$ elements can be encoded in uncompressed form (the x-coordinate followed by the y-coordinate) or in compressed form (just the x-coordinate). $\mathbb{G}_1$ elements occupy 96 bytes in uncompressed form, and 48 bytes in compressed form. $\mathbb{G}_2$ elements occupy 192 bytes in uncompressed form, and 96 bytes in compressed form.

The most-significant three bits of a $\mathbb{G}_1$ or $\mathbb{G}_2$ encoding should be masked away before the coordinate(s) are interpreted. These bits are used to unambiguously represent the underlying element:

- The most significant bit, when set, indicates that the point is in compressed form. Otherwise, the point is in uncompressed form.
- The second-most significant bit indicates that the point is at infinity. If this bit is set, the remaining bits of the group element’s encoding should be set to zero.
- The third-most significant bit is set if (and only if) this point is in
compressed form
*and*it is not the point at infinity*and*its y-coordinate is the lexicographically largest of the two associated with the encoded x-coordinate.