hemera/reference/field.md

Goldilocks fieldHemera field
cyber cip entity cyber
π 0.0%

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
A physical quantity assigned to every point in spacetime, mediating forces and interactions. gravitational field: generated by mass, described by gravity and general relativity electromagnetic field: generated by charges and currents — see electromagnetism quantum fields: fundamental entities in…
trident/src/field
field
nebu/reference/field
field specification the Goldilocks prime field. arithmetic substrate for hemera, trident, nox, and every computational domain in cyber. the prime the Goldilocks prime. the name comes from its structure: a 64-bit prime with a 32-bit "hole" that enables fast reduction. reduction identity define the…

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