package bigmod
import "crypto/internal/fips140/bigmod"
Index
- type Modulus
-
type Nat
- func NewNat() *Nat
- func (x *Nat) Add(y *Nat, m *Modulus) *Nat
- func (x *Nat) BitLenVarTime() int
- func (x *Nat) Bits() []uint
- func (x *Nat) Bytes(m *Modulus) []byte
- func (x *Nat) DivShortVarTime(y uint) uint
- func (x *Nat) Equal(y *Nat) choice
- func (out *Nat) Exp(x *Nat, e []byte, m *Modulus) *Nat
- func (out *Nat) ExpShortVarTime(x *Nat, e uint, m *Modulus) *Nat
- func (x *Nat) ExpandFor(m *Modulus) *Nat
- func (x *Nat) GCDVarTime(a, b *Nat) (*Nat, error)
- func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool)
- func (x *Nat) IsMinusOne(m *Modulus) choice
- func (x *Nat) IsOdd() choice
- func (x *Nat) IsOne() choice
- func (x *Nat) IsZero() choice
- func (out *Nat) Mod(x *Nat, m *Modulus) *Nat
- func (x *Nat) Mul(y *Nat, m *Modulus) *Nat
- func (x *Nat) SetBytes(b []byte, m *Modulus) (*Nat, error)
- func (x *Nat) SetOverflowingBytes(b []byte, m *Modulus) (*Nat, error)
- func (x *Nat) SetUint(y uint) *Nat
- func (x *Nat) ShiftRightVarTime(n uint) *Nat
- func (x *Nat) Sub(y *Nat, m *Modulus) *Nat
- func (x *Nat) SubOne(m *Modulus) *Nat
- func (x *Nat) TrailingZeroBitsVarTime() uint
Types
type Modulus
type Modulus struct { // contains filtered or unexported fields }
Modulus is used for modular arithmetic, precomputing relevant constants.
A Modulus can leak the exact number of bits needed to store its value and is stored without padding. Its actual value is still kept secret.
func NewModulus
func NewModulus(b []byte) (*Modulus, error)
NewModulus creates a new Modulus from a slice of big-endian bytes. The modulus must be greater than one.
The number of significant bits and whether the modulus is even is leaked through timing side-channels.
func NewModulusProduct
func NewModulusProduct(a, b []byte) (*Modulus, error)
NewModulusProduct creates a new Modulus from the product of two numbers represented as big-endian byte slices. The result must be greater than one.
func (*Modulus) BitLen
func (m *Modulus) BitLen() int
BitLen returns the size of m in bits.
func (*Modulus) Nat
func (m *Modulus) Nat() *Nat
Nat returns m as a Nat.
func (*Modulus) Size
func (m *Modulus) Size() int
Size returns the size of m in bytes.
type Nat
type Nat struct { // contains filtered or unexported fields }
Nat represents an arbitrary natural number
Each Nat has an announced length, which is the number of limbs it has stored. Operations on this number are allowed to leak this length, but will not leak any information about the values contained in those limbs.
func NewNat
func NewNat() *Nat
NewNat returns a new nat with a size of zero, just like new(Nat), but with the preallocated capacity to hold a number of up to preallocTarget bits. NewNat inlines, so the allocation can live on the stack.
func (*Nat) Add
func (x *Nat) Add(y *Nat, m *Modulus) *Nat
Add computes x = x + y mod m.
The length of both operands must be the same as the modulus. Both operands must already be reduced modulo m.
func (*Nat) BitLenVarTime
func (x *Nat) BitLenVarTime() int
BitLenVarTime returns the actual size of x in bits.
The actual size of x (but nothing more) leaks through timing side-channels. Note that this is ordinarily secret, as opposed to the announced size of x.
func (*Nat) Bits
func (x *Nat) Bits() []uint
Bits returns x as a little-endian slice of uint. The length of the slice matches the announced length of x. The result and x share the same underlying array.
func (*Nat) Bytes
func (x *Nat) Bytes(m *Modulus) []byte
Bytes returns x as a zero-extended big-endian byte slice. The size of the slice will match the size of m.
x must have the same size as m and it must be less than or equal to m.
func (*Nat) DivShortVarTime
func (x *Nat) DivShortVarTime(y uint) uint
DivShortVarTime calculates x = x / y and returns the remainder.
It panics if y is zero.
func (*Nat) Equal
func (x *Nat) Equal(y *Nat) choice
Equal returns 1 if x == y, and 0 otherwise.
Both operands must have the same announced length.
func (*Nat) Exp
func (out *Nat) Exp(x *Nat, e []byte, m *Modulus) *Nat
Exp calculates out = x^e mod m.
The exponent e is represented in big-endian order. The output will be resized to the size of m and overwritten. x must already be reduced modulo m.
m must be odd, or Exp will panic.
func (*Nat) ExpShortVarTime
func (out *Nat) ExpShortVarTime(x *Nat, e uint, m *Modulus) *Nat
ExpShortVarTime calculates out = x^e mod m.
The output will be resized to the size of m and overwritten. x must already be reduced modulo m. This leaks the exponent through timing side-channels.
m must be odd, or ExpShortVarTime will panic.
func (*Nat) ExpandFor
func (x *Nat) ExpandFor(m *Modulus) *Nat
ExpandFor ensures x has the right size to work with operations modulo m.
The announced size of x must be smaller than or equal to that of m.
func (*Nat) GCDVarTime
func (x *Nat) GCDVarTime(a, b *Nat) (*Nat, error)
GCDVarTime calculates x = GCD(a, b) where at least one of a or b is odd, and both are non-zero. If GCDVarTime returns an error, x is not modified.
The output will be resized to the size of the larger of a and b.
func (*Nat) InverseVarTime
func (x *Nat) InverseVarTime(a *Nat, m *Modulus) (*Nat, bool)
InverseVarTime calculates x = a⁻¹ mod m and returns (x, true) if a is invertible. Otherwise, InverseVarTime returns (x, false) and x is not modified.
a must be reduced modulo m, but doesn't need to have the same size. The output will be resized to the size of m and overwritten.
func (*Nat) IsMinusOne
func (x *Nat) IsMinusOne(m *Modulus) choice
IsMinusOne returns 1 if x == -1 mod m, and 0 otherwise.
The length of x must be the same as the modulus. x must already be reduced modulo m.
func (*Nat) IsOdd
func (x *Nat) IsOdd() choice
IsOdd returns 1 if x is odd, and 0 otherwise.
func (*Nat) IsOne
func (x *Nat) IsOne() choice
IsOne returns 1 if x == 1, and 0 otherwise.
func (*Nat) IsZero
func (x *Nat) IsZero() choice
IsZero returns 1 if x == 0, and 0 otherwise.
func (*Nat) Mod
func (out *Nat) Mod(x *Nat, m *Modulus) *Nat
Mod calculates out = x mod m.
This works regardless how large the value of x is.
The output will be resized to the size of m and overwritten.
func (*Nat) Mul
func (x *Nat) Mul(y *Nat, m *Modulus) *Nat
Mul calculates x = x * y mod m.
The length of both operands must be the same as the modulus. Both operands must already be reduced modulo m.
func (*Nat) SetBytes
func (x *Nat) SetBytes(b []byte, m *Modulus) (*Nat, error)
SetBytes assigns x = b, where b is a slice of big-endian bytes. SetBytes returns an error if b >= m.
The output will be resized to the size of m and overwritten.
func (*Nat) SetOverflowingBytes
func (x *Nat) SetOverflowingBytes(b []byte, m *Modulus) (*Nat, error)
SetOverflowingBytes assigns x = b, where b is a slice of big-endian bytes. SetOverflowingBytes returns an error if b has a longer bit length than m, but reduces overflowing values up to 2^⌈log2(m)⌉ - 1.
The output will be resized to the size of m and overwritten.
func (*Nat) SetUint
func (x *Nat) SetUint(y uint) *Nat
SetUint assigns x = y.
The output will be resized to a single limb and overwritten.
func (*Nat) ShiftRightVarTime
func (x *Nat) ShiftRightVarTime(n uint) *Nat
ShiftRightVarTime sets x = x >> n.
The announced length of x is unchanged.
func (*Nat) Sub
func (x *Nat) Sub(y *Nat, m *Modulus) *Nat
Sub computes x = x - y mod m.
The length of both operands must be the same as the modulus. Both operands must already be reduced modulo m.
func (*Nat) SubOne
func (x *Nat) SubOne(m *Modulus) *Nat
SubOne computes x = x - 1 mod m.
The length of x must be the same as the modulus.
func (*Nat) TrailingZeroBitsVarTime
func (x *Nat) TrailingZeroBitsVarTime() uint
TrailingZeroBitsVarTime returns the number of trailing zero bits in x.