Package: crypto/internal/edwards25519/field

package field Import Path crypto/internal/edwards25519/field (on go.dev) Dependency Relation imports 4 packages, and imported by 2 packages Involved Source Files d fe.go Package field implements fast arithmetic modulo 2^255-19. fe_amd64.go fe_arm64_noasm.go fe_generic.go fe_amd64.s Package-Level Type Names (total 2, in which 1 is exported) /* sort exporteds by: alphabet | popularity */ type Element (struct) Element represents an element of the field GF(2^255-19). Note that this is not a cryptographically secure group, and should only be used to interact with edwards25519.Point coordinates. This type works similarly to math/big.Int, and all arguments and receivers are allowed to alias. The zero value is a valid zero element. Fields (total 5, none are exported) /* 5 unexporteds ... *//* 5 unexporteds: */ l0 uint64 An element t represents the integer t.l0 + t.l1*2^51 + t.l2*2^102 + t.l3*2^153 + t.l4*2^204 Between operations, all limbs are expected to be lower than 2^52. l1 uint64 l2 uint64 l3 uint64 l4 uint64 Methods (total 23, in which 19 are exported) (*Element) Absolute(u *Element) *Element Absolute sets v to |u|, and returns v. (*Element) Add(a, b *Element) *Element Add sets v = a + b, and returns v. (*Element) Bytes() []byte Bytes returns the canonical 32-byte little-endian encoding of v. (*Element) Equal(u *Element) int Equal returns 1 if v and u are equal, and 0 otherwise. (*Element) Invert(z *Element) *Element Invert sets v = 1/z mod p, and returns v. If z == 0, Invert returns v = 0. (*Element) IsNegative() int IsNegative returns 1 if v is negative, and 0 otherwise. (*Element) Mult32(x *Element, y uint32) *Element Mult32 sets v = x * y, and returns v. (*Element) Multiply(x, y *Element) *Element Multiply sets v = x * y, and returns v. (*Element) Negate(a *Element) *Element Negate sets v = -a, and returns v. (*Element) One() *Element One sets v = 1, and returns v. (*Element) Pow22523(x *Element) *Element Pow22523 set v = x^((p-5)/8), and returns v. (p-5)/8 is 2^252-3. (*Element) Select(a, b *Element, cond int) *Element Select sets v to a if cond == 1, and to b if cond == 0. (*Element) Set(a *Element) *Element Set sets v = a, and returns v. (*Element) SetBytes(x []byte) (*Element, error) SetBytes sets v to x, where x is a 32-byte little-endian encoding. If x is not of the right length, SetBytes returns nil and an error, and the receiver is unchanged. Consistent with RFC 7748, the most significant bit (the high bit of the last byte) is ignored, and non-canonical values (2^255-19 through 2^255-1) are accepted. Note that this is laxer than specified by RFC 8032, but consistent with most Ed25519 implementations. (*Element) SqrtRatio(u, v *Element) (R *Element, wasSquare int) SqrtRatio sets r to the non-negative square root of the ratio of u and v. If u/v is square, SqrtRatio returns r and 1. If u/v is not square, SqrtRatio sets r according to Section 4.3 of draft-irtf-cfrg-ristretto255-decaf448-00, and returns r and 0. (*Element) Square(x *Element) *Element Square sets v = x * x, and returns v. (*Element) Subtract(a, b *Element) *Element Subtract sets v = a - b, and returns v. (*Element) Swap(u *Element, cond int) Swap swaps v and u if cond == 1 or leaves them unchanged if cond == 0, and returns v. (*Element) Zero() *Element Zero sets v = 0, and returns v. /* 4 unexporteds ... *//* 4 unexporteds: */ (*Element) bytes(out *[32]byte) []byte (*Element) carryPropagate() *Element (*Element) carryPropagateGeneric() *Element carryPropagateGeneric brings the limbs below 52 bits by applying the reduction identity (a * 2²⁵⁵ + b = a * 19 + b) to the l4 carry. (*Element) reduce() *Element reduce reduces v modulo 2^255 - 19 and returns it. As Outputs Of (at least 18, in which 15 are exported) func (*Element).Absolute(u *Element) *Element func (*Element).Add(a, b *Element) *Element func (*Element).Invert(z *Element) *Element func (*Element).Mult32(x *Element, y uint32) *Element func (*Element).Multiply(x, y *Element) *Element func (*Element).Negate(a *Element) *Element func (*Element).One() *Element func (*Element).Pow22523(x *Element) *Element func (*Element).Select(a, b *Element, cond int) *Element func (*Element).Set(a *Element) *Element func (*Element).SetBytes(x []byte) (*Element, error) func (*Element).SqrtRatio(u, v *Element) (R *Element, wasSquare int) func (*Element).Square(x *Element) *Element func (*Element).Subtract(a, b *Element) *Element func (*Element).Zero() *Element /* 3+ unexporteds ... *//* 3+ unexporteds: */ func (*Element).carryPropagate() *Element func (*Element).carryPropagateGeneric() *Element func (*Element).reduce() *Element As Inputs Of (at least 22, in which 14 are exported) func (*Element).Absolute(u *Element) *Element func (*Element).Add(a, b *Element) *Element func (*Element).Equal(u *Element) int func (*Element).Invert(z *Element) *Element func (*Element).Mult32(x *Element, y uint32) *Element func (*Element).Multiply(x, y *Element) *Element func (*Element).Negate(a *Element) *Element func (*Element).Pow22523(x *Element) *Element func (*Element).Select(a, b *Element, cond int) *Element func (*Element).Set(a *Element) *Element func (*Element).SqrtRatio(u, v *Element) (R *Element, wasSquare int) func (*Element).Square(x *Element) *Element func (*Element).Subtract(a, b *Element) *Element func (*Element).Swap(u *Element, cond int) /* 8+ unexporteds ... *//* 8+ unexporteds: */ func feMul(out *Element, a *Element, b *Element) func feMul(out *Element, a *Element, b *Element) func feMul(out *Element, a *Element, b *Element) func feMulGeneric(v, a, b *Element) func feSquare(out *Element, a *Element) func feSquare(out *Element, a *Element) func feSquareGeneric(v, a *Element) func crypto/internal/edwards25519.copyFieldElement(buf *[32]byte, v *Element) []byte As Types Of (total 6, none are exported) /* 6 unexporteds ... *//* 6 unexporteds: */ var feOne *Element var feZero *Element var sqrtM1 *Element var crypto/internal/edwards25519.d *Element var crypto/internal/edwards25519.d2 *Element var crypto/internal/edwards25519.feOne *Element /* one unexported ... *//* one unexported: */ type uint128 (struct) uint128 holds a 128-bit number as two 64-bit limbs, for use with the bits.Mul64 and bits.Add64 intrinsics. Fields (total 2, neither is exported) /* 2 unexporteds ... *//* 2 unexporteds: */ hi uint64 lo uint64 As Outputs Of (at least 2, neither is exported) /* 2+ unexporteds ... *//* 2+ unexporteds: */ func addMul64(v uint128, a, b uint64) uint128 func mul64(a, b uint64) uint128 As Inputs Of (at least 2, neither is exported) /* 2+ unexporteds ... *//* 2+ unexporteds: */ func addMul64(v uint128, a, b uint64) uint128 func shiftRightBy51(a uint128) uint64 Package-Level Functions (total 9, none are exported) /* 9 unexporteds ... *//* 9 unexporteds: */ func addMul64(v uint128, a, b uint64) uint128 addMul64 returns v + a * b. func feMul(out *Element, a *Element, b *Element) feMul sets out = a * b. It works like feMulGeneric. func feMulGeneric(v, a, b *Element) func feSquare(out *Element, a *Element) feSquare sets out = a * a. It works like feSquareGeneric. func feSquareGeneric(v, a *Element) func mask64Bits(cond int) uint64 mask64Bits returns 0xffffffff if cond is 1, and 0 otherwise. func mul51(a uint64, b uint32) (lo uint64, hi uint64) mul51 returns lo + hi * 2⁵¹ = a * b. func mul64(a, b uint64) uint128 mul64 returns a * b. func shiftRightBy51(a uint128) uint64 shiftRightBy51 returns a >> 51. a is assumed to be at most 115 bits. Package-Level Variables (total 3, none are exported) /* 3 unexporteds ... *//* 3 unexporteds: */ var feOne *Element var feZero *Element var sqrtM1 *Element sqrtM1 is 2^((p-1)/4), which squared is equal to -1 by Euler's Criterion. Package-Level Constants (only one, which is unexported) /* one unexported ... *//* one unexported: */ const maskLow51Bits uint64 = 2251799813685247

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