field specification
the Goldilocks prime field specification lives in nebu: the standalone field arithmetic library.
canonical source: ~/git/nebu/reference/field.md
summary
all Hemera arithmetic operates over the Goldilocks prime field:
p = 2⁶⁴ − 2³² + 1 = 0xFFFFFFFF00000001
the field provides native u64 arithmetic, two-adicity of 32 for NTT, and the minimum invertible S-box exponent d = 7. see nebu/reference/field for the complete specification: arithmetic operations, properties, NTT compatibility, encoding rules, and hardware support.
Hemera-specific usage
- S-box exponent: d = 7 (minimum invertible for this field). see permutation.
- encoding: 7 bytes per field element, little-endian. see encoding.
- MDS matrices: M_E and M_I are defined over this field. see matrices.
- round constants: 192 elements of this field. see constants.
Dimensions
field
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kuro/specs/field
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nebu/specs/field
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trident/src/field
field
nebu/reference/field