bits

Documentation

Index

• func AssertIsTrit(api frontend.API, v frontend.Variable)
• func FromBase(api frontend.API, base Base, digits []frontend.Variable, ...) frontend.Variable
• func FromBinary(api frontend.API, digits []frontend.Variable, opts ...BaseConversionOption) frontend.Variable
• func FromTernary(api frontend.API, digits []frontend.Variable, opts ...BaseConversionOption) frontend.Variable
• func GetHints() []solver.Hint
• func ToBase(api frontend.API, base Base, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable
• func ToBinary(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable
• func ToNAF(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable
• func ToTernary(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable
• type Base
• type BaseConversionOption
  • func OmitModulusCheck() BaseConversionOption
  • func WithNbDigits(nbDigits int) BaseConversionOption
  • func WithUnconstrainedInputs() BaseConversionOption
  • func WithUnconstrainedOutputs() BaseConversionOption

Functions

func AssertIsTrit

func AssertIsTrit(api frontend.API, v frontend.Variable)

AssertIsTrit constrains digit to be 0, 1 or 2.

func FromBase

func FromBase(api frontend.API, base Base, digits []frontend.Variable, opts ...BaseConversionOption) frontend.Variable

FromBase compute from a set of digits its canonical representation in little-endian order. For example for base 2, it returns Σbi = Σ (2**i * digits[i])

func FromBinary

func FromBinary(api frontend.API, digits []frontend.Variable, opts ...BaseConversionOption) frontend.Variable

FromBinary is an alias of FromBase(api, Binary, digits)

func FromTernary

func FromTernary(api frontend.API, digits []frontend.Variable, opts ...BaseConversionOption) frontend.Variable

FromTernary is an alias of FromBase(api, Ternary, digits)

func GetHints

func GetHints() []solver.Hint

func ToBase

func ToBase(api frontend.API, base Base, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable

ToBase decomposes scalar v into digits in given base using options opts. The decomposition is in little-endian order.

func ToBinary

func ToBinary(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable

ToBinary is an alias of ToBase(api, Binary, v, opts)

func ToNAF

func ToNAF(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable

ToNAF returns the NAF decomposition of given input. The non-adjacent form (NAF) of a number is a unique signed-digit representation, in which non-zero values cannot be adjacent. For example, NAF(13) = [1, 0, -1, 0, 1].

func ToTernary

func ToTernary(api frontend.API, v frontend.Variable, opts ...BaseConversionOption) []frontend.Variable

ToTernary is an alias of ToBase(api, Ternary, v, opts...)

Types

type Base

type Base uint8

Base defines the base for decomposing the scalar into digits.

const (
	// Binary base decomposes scalar into bits (0-1)
	Binary Base = 2

	// Ternary base decomposes scalar into trits (0-1-2)
	Ternary Base = 3
)

type BaseConversionOption

type BaseConversionOption func(opt *baseConversionConfig) error

BaseConversionOption configures the behaviour of scalar decomposition.

func OmitModulusCheck

func OmitModulusCheck() BaseConversionOption

OmitModulusCheck omits the comparison against native field modulus in case the bitlength of the decomposed value (if WithNbDigits not set or set to bitlength of the native modulus) eqals bitlength of the modulus.

The check is otherwise required as there are possibly multiple correct binary decompositions. For example, when decomposing small a the decomposition could return the slices for both a or a+r, where r is the native modulus and the enforced constraints are correct due to implicit modular reduction by r.

This option can be used in case the decomposed output is manually checked to be unique or if uniqueness is not required.

func WithNbDigits

func WithNbDigits(nbDigits int) BaseConversionOption

WithNbDigits sets the resulting number of digits (nbDigits) to be used in the base conversion.

nbDigits must be > 0. If nbDigits is lower than the length of full decomposition and WithUnconstrainedOutputs option is not used, then the conversion functions will generate an unsatisfiable constraint.

If nbDigits is larger than the bitlength of the modulus, then the returned slice has length nbDigits with excess bits being 0.

If WithNbDigits option is not set, then the full decomposition is returned.

func WithUnconstrainedInputs

func WithUnconstrainedInputs() BaseConversionOption

WithUnconstrainedInputs indicates to the FromBase apis to constrain its inputs (digits) to ensure they are valid digits in base b. For example, FromBinary without this option will add 1 constraint per bit to ensure it is either 0 or 1.

func WithUnconstrainedOutputs

func WithUnconstrainedOutputs() BaseConversionOption

WithUnconstrainedOutputs sets the bit conversion API to NOT constrain the output bits. This is UNSAFE but is useful when the outputs are already constrained by other circuit constraints. The sum of the digits will is constrained like so Σbi = Σ (base**i * digits[i]) But the individual digits are not constrained to be valid digits in base b.