Module point 

Edwards-point arithmetic, scalar multiplication, and point encoding.

This module re-exports the point controller, balanced-radix-16 scalar multiplier, strict compression/decompression controller, and the constant-time 32-byte equality kernel used by verification.

Modules

parallel_point

Level-scheduled Edwards formulas over four field engines.

Structs

EdwardsPoint

Extended Edwards point (X:Y:Z:T) over FieldElement2625.

ParallelPointOpController

Four-lane level scheduler for extended Edwards formulas.

ParallelPointOpControllerIn

Point request plus four shared field-lane responses.

ParallelPointOpControllerOut

Point response plus commands for four shared field lanes.

ParallelPointOpRegs

Registered operation, formula-level, lane-mask, and identity state.

PointCodecController

Point-codec controller using field exponentiation, canonical codec, and a shared field-multiplier response.

PointCodecControllerIn

External point-codec command plus shared field-multiplier response.

PointCodecControllerOut

External point-codec response plus shared field-multiplier command.

PointCodecEngine

Self-contained point codec with a private parallel field multiplier.

PointCodecIn

Point-codec command.

PointCodecOut

Point-codec response.

PointControlRegs

Registered control state for PointOpController.

PointMicroInstruction

Decoded 16-bit point-formula microinstruction.

PointOpController

Serial microcoded point-operation controller using a shared field engine.

PointOpControllerIn

External command and shared field-multiplier response.

PointOpControllerOut

External response and shared field-multiplier command.

PointOpEngine

Self-contained point engine using the four-lane parallel controller/bank.

PointOpIn

Point operation or one-word Niels-table load request.

PointOpOut

Point-operation response and retained point views.

ProjectiveNielsPoint

Cached Projective Niels representation used by mixed addition.

ScalarMulController

Controller with eight identically addressed local Niels-table BRAM banks.

ScalarMulControllerIn

Scalar command plus response from the shared point controller.

ScalarMulControllerOut

Scalar response plus command for the shared point controller.

ScalarMulEngine

Self-contained scalar multiplier using a private point-operation engine.

ScalarMulIn

Scalar-multiplication request.

ScalarMulOut

Scalar-multiplication response and constant-pattern instrumentation.

ScalarMulRegs

Registered recoding, table address, digit, and instrumentation state.

Enums

ParallelPointOpState

Formula launch, wait, and completion states.

PointOpState

Fetch, launch, wait, and completion states of PointOpController.

ScalarMulState

Table-generation, recoding, fixed scan, point-operation, and completion states.

Constants

CODEC_COMPRESS_INV

Invert projective Z during compression.

CODEC_COMPRESS_X

Multiply X by Z^-1.

CODEC_COMPRESS_X_ENCODE

Encode affine x to obtain its parity bit.

CODEC_COMPRESS_Y

Multiply Y by Z^-1.

CODEC_COMPRESS_Y_ENCODE

Encode affine y and attach the x parity bit.

CODEC_DECOMPRESS_ADJUST

Adjust the root by sqrt(-1) when required.

CODEC_DECOMPRESS_CANDIDATE_ENCODE

Encode the candidate to determine sign and zero properties.

CODEC_DECOMPRESS_CANONICAL

Decode y and begin canonicality validation.

CODEC_DECOMPRESS_CANONICAL_COMPARE

Re-encode decoded y for canonical comparison.

CODEC_DECOMPRESS_CHECK

Check the candidate against the curve equation.

CODEC_DECOMPRESS_CHECK_COMPARE

Compare canonical root-check encodings.

CODEC_DECOMPRESS_CHECK_ENCODE_LEFT

Encode the left side of the root check.

CODEC_DECOMPRESS_CHECK_ENCODE_RIGHT

Encode the right side of the root check.

CODEC_DECOMPRESS_DY2

Compute d*y^2.

CODEC_DECOMPRESS_NEGATE

Negate x to match the encoded sign bit.

CODEC_DECOMPRESS_SQRT

Compute a fixed-chain square-root candidate.

CODEC_DECOMPRESS_T

Compute extended coordinate T = X*Y with Z = 1.

CODEC_DECOMPRESS_U

Compute numerator u = y^2 - 1.

CODEC_DECOMPRESS_V

Compute denominator v = d*y^2 + 1.

CODEC_DECOMPRESS_V_INV

Invert v.

CODEC_DECOMPRESS_X2

Compute x^2 = u/v.

CODEC_DECOMPRESS_Y2

Compute y^2.

CODEC_DONE

Present a completed codec result.

CODEC_IDLE

Waiting for a compression/decompression command.

POINT_CODEC_COMPRESS

Compress an extended point to 32-byte Edwards-Y form.

POINT_CODEC_DECOMPRESS

Strictly decompress a 32-byte Edwards-Y encoding.

POINT_OP_ADD_NIELS

Add a Projective Niels point to an extended Edwards point.

POINT_OP_DOUBLE

Double an extended Edwards point.

POINT_OP_IS_IDENTITY

Test whether an extended point represents the identity.

POINT_OP_TO_NIELS

Convert an extended point into Projective Niels form.

Functions

bytes32_equal_kernel

Compare all bytes of two 32-byte arrays with a fixed boolean structure.

ed25519_basepoint

Return the canonical Ed25519 base point in extended coordinates.

ed25519_basepoint_kernel

Synthesizable Ed25519 base-point constructor.

edwards_d2_kernel

Return Edwards25519 curve constant 2*d.

edwards_d_kernel

Return Edwards25519 curve constant d.

edwards_identity

Return the extended identity (0:1:1:0).

edwards_identity_kernel

Synthesizable extended-identity constructor.

get_field_limb_kernel

Read one limb from a field element using a digital limb index.

negate_niels_kernel

Negate a Projective Niels point without inversion.

negate_point_kernel

Negate an extended Edwards point.

niels_identity

Return the Projective Niels identity.

niels_identity_kernel

Synthesizable Projective Niels identity constructor.

niels_word_kernel

Read one of the forty 32-bit words in a Projective Niels point.

parallel_point_op_controller_kernel

Next-state/output kernel for ParallelPointOpController.

point_codec_controller_kernel

Next-state/output kernel for PointCodecController.

point_codec_engine_kernel

Wires PointCodecController to its private field multiplier.

point_codec_initial_regs

Return the idle point-codec register tuple.

point_decode_instruction_kernel

Decode one packed point microinstruction.

point_identity_registers

Return the nine retained microcode registers initialized to point identities.

point_instruction_address_kernel

Map a point operation and step to the microcode ROM address.

point_load_registers_kernel

Load point/Niels operands into the microcode register file.

point_op_controller_kernel

Next-state/output kernel for PointOpController.

point_op_engine_kernel

Wires ParallelPointOpController to ParallelFieldMulBank4.

point_select_register_kernel

Select a field operand from the point register file or constant sources.

point_write_register_kernel

Write one field result to the selected point register.

scalar_mul_controller_kernel

Next-state/output kernel for ScalarMulController.

scalar_mul_engine_kernel

Wires ScalarMulController to its private point-operation engine.

set_field_limb_kernel

Replace one limb in a field element using a digital limb index.

set_niels_word_kernel

Replace one of the forty 32-bit words in a Projective Niels point.

sqrt_m1_kernel

Return the field square root of -1 used by point decompression.

Type Aliases

PointCodecAction

Mutable register/child-command action returned by a transition sub-kernel.

PointCodecContext

Read-only context supplied to each codec transition sub-kernel.

PointCodecRegs

Compact retained codec state: state, three field temporaries, and flags.

PointCodecState

Five-bit point-codec state encoding.