X448

Documentation

Index

• Constants
• Variables
• func AuthDecap(config_id int, skR []byte, pkE []byte, pkR []byte, pkS []byte) []byte
• func AuthEncap(config_id int, skE []byte, skS []byte, pkE []byte, pkR []byte, pkS []byte) []byte
• func Comp(a *BIG, b *BIG) int
• func Decap(config_id int, skR []byte, pkE []byte, pkR []byte) []byte
• func DeriveKeyPair(config_id int, SK []byte, PK []byte, SEED []byte) bool
• func ECDH_ECIES_DECRYPT(sha int, P1 []byte, P2 []byte, V []byte, C []byte, T []byte, U []byte) []byte
• func ECDH_ECIES_ENCRYPT(sha int, P1 []byte, P2 []byte, RNG *core.RAND, W []byte, M []byte, V []byte, ...) []byte
• func ECDH_ECPSP_DSA(sha int, RNG *core.RAND, S []byte, F []byte, C []byte, D []byte) int
• func ECDH_ECPSVDP_DH(S []byte, WD []byte, Z []byte, typ int) int
• func ECDH_ECPVP_DSA(sha int, W []byte, F []byte, C []byte, D []byte) int
• func ECDH_IN_RANGE(S []byte) bool
• func ECDH_KEY_PAIR_GENERATE(RNG *core.RAND, S []byte, W []byte) int
• func ECDH_PUBLIC_KEY_VALIDATE(W []byte) int
• func Encap(config_id int, skE []byte, pkE []byte, pkR []byte) []byte
• func FP_tpo(i *FP, s *FP) int
• func KEY_PAIR_GENERATE(RNG *core.RAND, D []byte, Q []byte) int
• func KeySchedule(config_id int, mode int, Z []byte, info []byte, psk []byte, pskID []byte) ([]byte, []byte, []byte)
• func RFC7748(r *BIG)
• func SIGNATURE(ph bool, D []byte, ctx []byte, M []byte, SIG []byte) int
• func VERIFY(ph bool, Q []byte, ctx []byte, M []byte, SIG []byte) bool
• type BIG
  • func BIG_frombytearray(b []byte, n int) *BIG
  • func FromBytes(b []byte) *BIG
  • func Modadd(a1, b1, m *BIG) *BIG
  • func Modmul(a1, b1, m *BIG) *BIG
  • func Modneg(a1, m *BIG) *BIG
  • func Modsqr(a1, m *BIG) *BIG
  • func NewBIG() *BIG
  • func NewBIGcopy(x *BIG) *BIG
  • func NewBIGdcopy(x *DBIG) *BIG
  • func NewBIGint(x int) *BIG
  • func NewBIGints(x [NLEN]Chunk) *BIG
  • func Random(rng *core.RAND) *BIG
  • func Randomnum(q *BIG, rng *core.RAND) *BIG
  • func Randtrunc(q *BIG, trunc int, rng *core.RAND) *BIG
  • func (r *BIG) Invmodp(p *BIG)
  • func (r *BIG) Jacobi(p *BIG) int
  • func (r *BIG) Minus(x *BIG) *BIG
  • func (r *BIG) Mod(m *BIG)
  • func (r *BIG) Nbits() int
  • func (r *BIG) Plus(x *BIG) *BIG
  • func (r *BIG) Powmod(e1 *BIG, m *BIG) *BIG
  • func (r *BIG) ToBytes(b []byte)
  • func (r *BIG) ToString() string
• type Chunk
• type DBIG
  • func DBIG_fromBytes(b []byte) *DBIG
  • func NewDBIG() *DBIG
  • func NewDBIGcopy(x *DBIG) *DBIG
  • func NewDBIGscopy(x *BIG) *DBIG
  • func (r *DBIG) Mod(m *BIG) *BIG
• type ECP
  • func ECP_fromBytes(b []byte) *ECP
  • func ECP_generator() *ECP
  • func ECP_hap2point(h *BIG) *ECP
  • func ECP_map2point(h *FP) *ECP
  • func ECP_mapit(h []byte) *ECP
  • func ECP_muln(n int, X []*ECP, e []*BIG) *ECP
  • func NewECP() *ECP
  • func NewECPbig(ix *BIG) *ECP
  • func NewECPbigint(ix *BIG, s int) *ECP
  • func NewECPbigs(ix *BIG, iy *BIG) *ECP
  • func (E *ECP) Add(Q *ECP)
  • func (E *ECP) Affine()
  • func (E *ECP) Cfp()
  • func (E *ECP) Copy(P *ECP)
  • func (E *ECP) Equals(Q *ECP) bool
  • func (E *ECP) GetS() int
  • func (E *ECP) GetX() *BIG
  • func (E *ECP) GetY() *BIG
  • func (E *ECP) Is_infinity() bool
  • func (E *ECP) Mul(e *BIG) *ECP
  • func (E *ECP) Mul2(e *BIG, Q *ECP, f *BIG) *ECP
  • func (E *ECP) Neg()
  • func (E *ECP) Sub(Q *ECP)
  • func (E *ECP) ToBytes(b []byte, compress bool)
  • func (E *ECP) ToString() string
• type FP
  • func FP_fromBytes(b []byte) *FP
  • func NewFP() *FP
  • func NewFPbig(a *BIG) *FP
  • func NewFPcopy(a *FP) *FP
  • func NewFPint(a int) *FP
  • func NewFPrand(rng *core.RAND) *FP
  • func RHS(x *FP) *FP
  • func (F *FP) Equals(a *FP) bool
  • func (F *FP) ToBytes(b []byte)
  • func (F *FP) ToString() string

Constants

const AESKEY int = 32

const ALLOW_ALT_COMPRESS bool = false

const ATE_BITS int = NOT

const BASEBITS uint = 58

const BIGBITS int = int(MODBYTES * 8)

const BIG_ENDIAN_SIGN bool = false

const BLS12 int = 2

const BLS24 int = 3

const BLS48 int = 4

const BN int = 1

const CHUNK int = 64 /* Set word size */

const CURVETYPE int = MONTGOMERY

const CURVE_A int = 156326

const CURVE_B_I int = 0

const CURVE_Cof_I int = 4

const CURVE_PAIRING_TYPE int = NOT

const DNLEN int = 2 * NLEN

const D_TYPE int = 0

Pairing Twist type

const ECDH_ERROR int = -3

const ECDH_INVALID_PUBLIC_KEY int = -2

const EDDSA_INVALID_PUBLIC_KEY int = -2

const EDWARDS int = 1

const EFS int = int(MODBYTES)

const INVALID int = -4

const EGS int = int(MODBYTES)

const FEXCESS int32 = ((int32(1) << 16) - 1)

const FP_DENSE int = 5

const FP_ONE int = 1

const FP_SPARSE int = 4

const FP_SPARSER int = 3

const FP_SPARSEST int = 2

const FP_ZERO int = 0

Sparsity

const G2_TABLE int = NOT

const GENERALISED_MERSENNE int = 3

const HASH_TYPE int = 64

const HBITS uint = (BASEBITS / 2)

const HTC_ISO int = 0

const HTC_ISO_G2 int = 0

const MODBITS uint = 448 /* Number of bits in Modulus */

Modulus details

const MODBYTES uint = 56

BIG length in bytes and number base

const MODTYPE int = GENERALISED_MERSENNE //NOT_SPECIAL

const MONTGOMERY int = 2

const MONTGOMERY_FRIENDLY int = 2

const M_TYPE int = 1

const NEGATIVEX int = 1

const NEGATOWER int = 0

const NEXCESS int = (1 << (uint(CHUNK) - BASEBITS - 1))

const NLEN int = int((1 + ((8*MODBYTES - 1) / BASEBITS)))

BIG lengths and Masks

const NOT int = 0

Pairing Friendly?

const NOT_SPECIAL int = 0

Modulus types

const PM1D2 uint = 1 /* Modulus mod 8 */

const POSITIVEX int = 0

Pairing x parameter sign

const POSITOWER int = 1

const PSEUDO_MERSENNE int = 1

const QNRI int = 0 // Fp2 QNR

const RIADZ int = 0 /* hash-to-point Z */

const RIADZG2A int = 0 /* G2 hash-to-point Z */

const RIADZG2B int = 0 /* G2 hash-to-point Z */

const SEXTIC_TWIST int = NOT

const SIGN_OF_X int = NOT

const TBITS uint = MODBITS % BASEBITS // Number of active bits in top word

const TOWER int = NEGATOWER // Tower type

const USE_GLV bool = true

const USE_GS_G2 bool = true

const USE_GS_GT bool = true

const WEIERSTRASS int = 0

Curve types

Variables

var CURVE_B = [...]Chunk{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}

var CURVE_Cof = [...]Chunk{0x4, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}

var CURVE_Gx = [...]Chunk{0x5, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}

var CURVE_Gy = [...]Chunk{0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0}

var CURVE_HTPC = [...]Chunk{0x3FFFFFFFFFFFFFE, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FBFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFF}

var CURVE_Order = [...]Chunk{0x378C292AB5844F3, 0x3309CA37163D548, 0x1B49AED63690216, 0x3FDF3288FA7113B, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0xFFFFFFFFFF}

var Modulus = [...]Chunk{0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FBFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFF}

Base Bits= 58

var R2modp = [...]Chunk{0x200000000, 0x0, 0x0, 0x0, 0x3000000, 0x0, 0x0, 0x0}

var ROI = [...]Chunk{0x3FFFFFFFFFFFFFE, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FBFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFFFFFF, 0x3FFFFFFFFFF}

Functions

func AuthDecap

func AuthDecap(config_id int, skR []byte, pkE []byte, pkR []byte, pkS []byte) []byte

func AuthEncap

func AuthEncap(config_id int, skE []byte, skS []byte, pkE []byte, pkR []byte, pkS []byte) []byte

func Comp

func Comp(a *BIG, b *BIG) int

Compare a and b, return 0 if a==b, -1 if a<b, +1 if a>b. Inputs must be normalised

func Decap

func Decap(config_id int, skR []byte, pkE []byte, pkR []byte) []byte

func DeriveKeyPair

func DeriveKeyPair(config_id int, SK []byte, PK []byte, SEED []byte) bool

func ECDH_ECIES_DECRYPT

func ECDH_ECIES_DECRYPT(sha int, P1 []byte, P2 []byte, V []byte, C []byte, T []byte, U []byte) []byte

IEEE1363 ECIES decryption. Decryption of ciphertext V,C,T using private key U outputs plaintext M

func ECDH_ECIES_ENCRYPT

func ECDH_ECIES_ENCRYPT(sha int, P1 []byte, P2 []byte, RNG *core.RAND, W []byte, M []byte, V []byte, T []byte) []byte

IEEE1363 ECIES encryption. Encryption of plaintext M uses public key W and produces ciphertext V,C,T

func ECDH_ECPSP_DSA

func ECDH_ECPSP_DSA(sha int, RNG *core.RAND, S []byte, F []byte, C []byte, D []byte) int

IEEE ECDSA Signature, C and D are signature on F using private key S

func ECDH_ECPSVDP_DH

func ECDH_ECPSVDP_DH(S []byte, WD []byte, Z []byte, typ int) int

IEEE-1363 Diffie-Hellman online calculation Z=S.WD

type = 0 is just x coordinate output type = 1 for standard compressed output type = 2 for standard uncompress output 04|x|y

func ECDH_ECPVP_DSA

func ECDH_ECPVP_DSA(sha int, W []byte, F []byte, C []byte, D []byte) int

IEEE1363 ECDSA Signature Verification. Signature C and D on F is verified using public key W

func ECDH_IN_RANGE

func ECDH_IN_RANGE(S []byte) bool

return true if S is in ranger 0 < S < order , else return false

func ECDH_KEY_PAIR_GENERATE

func ECDH_KEY_PAIR_GENERATE(RNG *core.RAND, S []byte, W []byte) int

Calculate a public/private EC GF(p) key pair W,S where W=S.G mod EC(p), * where S is the secret key and W is the public key * and G is fixed generator. * If RNG is NULL then the private key is provided externally in S * otherwise it is generated randomly internally

func ECDH_PUBLIC_KEY_VALIDATE

func ECDH_PUBLIC_KEY_VALIDATE(W []byte) int

validate public key

func Encap

func Encap(config_id int, skE []byte, pkE []byte, pkR []byte) []byte

func FP_tpo

func FP_tpo(i *FP, s *FP) int

Two for the price of one - See Hamburg https://eprint.iacr.org/2012/309.pdf Calculate inverse of i and square root of s, return QR

func KEY_PAIR_GENERATE

func KEY_PAIR_GENERATE(RNG *core.RAND, D []byte, Q []byte) int

Calculate a public/private EC GF(p) key pair. Q=D.G mod EC(p), * where D is the secret key and Q is the public key * and G is fixed generator. * RNG is a cryptographically strong RNG * If RNG==NULL, D is provided externally

func KeySchedule

func KeySchedule(config_id int, mode int, Z []byte, info []byte, psk []byte, pskID []byte) ([]byte, []byte, []byte)

func RFC7748

func RFC7748(r *BIG)

Transform a point multiplier to RFC7748 form

func SIGNATURE

func SIGNATURE(ph bool, D []byte, ctx []byte, M []byte, SIG []byte) int

Generate a signature using key pair (D,Q) on message M Set ph=true if message has already been pre-hashed if ph=false, then context should be NULL for ed25519. However RFC8032 mode ed25519ctx is supported by supplying a non-NULL or non-empty context

func VERIFY

func VERIFY(ph bool, Q []byte, ctx []byte, M []byte, SIG []byte) bool

Types

type BIG

type BIG struct {
	// contains filtered or unexported fields
}

func BIG_frombytearray

func BIG_frombytearray(b []byte, n int) *BIG

convert from byte array to BIG

func FromBytes

func FromBytes(b []byte) *BIG

func Modadd

func Modadd(a1, b1, m *BIG) *BIG

return a+b mod m

func Modmul

func Modmul(a1, b1, m *BIG) *BIG

return a*b mod m

func Modneg

func Modneg(a1, m *BIG) *BIG

return -a mod m

func Modsqr

func Modsqr(a1, m *BIG) *BIG

return a^2 mod m

func NewBIG

func NewBIG() *BIG

func NewBIGcopy

func NewBIGcopy(x *BIG) *BIG

func NewBIGdcopy

func NewBIGdcopy(x *DBIG) *BIG

func NewBIGint

func NewBIGint(x int) *BIG

func NewBIGints

func NewBIGints(x [NLEN]Chunk) *BIG

func Random

func Random(rng *core.RAND) *BIG

get 8*MODBYTES size random number

func Randomnum

func Randomnum(q *BIG, rng *core.RAND) *BIG

Create random BIG in portable way, one bit at a time

func Randtrunc

func Randtrunc(q *BIG, trunc int, rng *core.RAND) *BIG

func (*BIG) Invmodp

func (r *BIG) Invmodp(p *BIG)

this=1/this mod p. Binary method

func (*BIG) Jacobi

func (r *BIG) Jacobi(p *BIG) int

Jacobi Symbol (this/p). Returns 0, 1 or -1

func (*BIG) Minus

func (r *BIG) Minus(x *BIG) *BIG

return this-x

func (*BIG) Mod

func (r *BIG) Mod(m *BIG)

reduce this mod m

func (*BIG) Nbits

func (r *BIG) Nbits() int

func (*BIG) Plus

func (r *BIG) Plus(x *BIG) *BIG

return this+x

func (*BIG) Powmod

func (r *BIG) Powmod(e1 *BIG, m *BIG) *BIG

return this^e mod m

func (*BIG) ToBytes

func (r *BIG) ToBytes(b []byte)

func (*BIG) ToString

func (r *BIG) ToString() string

Convert to Hex String

type Chunk

type Chunk int64

const BMASK Chunk = ((Chunk(1) << BASEBITS) - 1)

const HMASK Chunk = ((Chunk(1) << HBITS) - 1)

const MConst Chunk = 0x1

const OMASK Chunk = ((Chunk(-1)) << (MODBITS % BASEBITS))

Modulus Masks

const TMASK Chunk = (Chunk(1) << TBITS) - 1

type DBIG

type DBIG struct {
	// contains filtered or unexported fields
}

func DBIG_fromBytes

func DBIG_fromBytes(b []byte) *DBIG

convert from byte array to BIG

func NewDBIG

func NewDBIG() *DBIG

func NewDBIGcopy

func NewDBIGcopy(x *DBIG) *DBIG

func NewDBIGscopy

func NewDBIGscopy(x *BIG) *DBIG

func (*DBIG) Mod

func (r *DBIG) Mod(m *BIG) *BIG

reduces this DBIG mod a BIG, and returns the BIG

type ECP

type ECP struct {
	// contains filtered or unexported fields
}

func ECP_fromBytes

func ECP_fromBytes(b []byte) *ECP

convert from byte array to point

func ECP_generator

func ECP_generator() *ECP

func ECP_hap2point

func ECP_hap2point(h *BIG) *ECP

Hunt and Peck a BIG to a curve point

func ECP_map2point

func ECP_map2point(h *FP) *ECP

Constant time Map to Point

func ECP_mapit

func ECP_mapit(h []byte) *ECP

func ECP_muln

func ECP_muln(n int, X []*ECP, e []*BIG) *ECP

Generic multi-multiplication, fixed 4-bit window, P=Sigma e_i*X_i

func NewECP

func NewECP() *ECP

Constructors

func NewECPbig

func NewECPbig(ix *BIG) *ECP

set from x - calculate y from curve equation

func NewECPbigint

func NewECPbigint(ix *BIG, s int) *ECP

set (x,y) from BIG and a bit

func NewECPbigs

func NewECPbigs(ix *BIG, iy *BIG) *ECP

set (x,y) from two BIGs

func (*ECP) Add

func (E *ECP) Add(Q *ECP)

this+=Q

func (*ECP) Affine

func (E *ECP) Affine()

set to affine - from (x,y,z) to (x,y)

func (*ECP) Cfp

func (E *ECP) Cfp()

func (*ECP) Copy

func (E *ECP) Copy(P *ECP)

this=P

func (*ECP) Equals

func (E *ECP) Equals(Q *ECP) bool

Test P == Q

func (*ECP) GetS

func (E *ECP) GetS() int

get sign of Y

func (*ECP) GetX

func (E *ECP) GetX() *BIG

extract x as a BIG

func (*ECP) GetY

func (E *ECP) GetY() *BIG

extract y as a BIG

func (*ECP) Is_infinity

func (E *ECP) Is_infinity() bool

test for O point-at-infinity

func (*ECP) Mul

func (E *ECP) Mul(e *BIG) *ECP

Public version

func (*ECP) Mul2

func (E *ECP) Mul2(e *BIG, Q *ECP, f *BIG) *ECP

func (*ECP) Neg

func (E *ECP) Neg()

this=-this

func (*ECP) Sub

func (E *ECP) Sub(Q *ECP)

this-=Q

func (*ECP) ToBytes

func (E *ECP) ToBytes(b []byte, compress bool)

convert to byte array

func (*ECP) ToString

func (E *ECP) ToString() string

convert to hex string

type FP

type FP struct {
	XES int32
	// contains filtered or unexported fields
}

func FP_fromBytes

func FP_fromBytes(b []byte) *FP

func NewFP

func NewFP() *FP

func NewFPbig

func NewFPbig(a *BIG) *FP

func NewFPcopy

func NewFPcopy(a *FP) *FP

func NewFPint

func NewFPint(a int) *FP

func NewFPrand

func NewFPrand(rng *core.RAND) *FP

func RHS

func RHS(x *FP) *FP

Calculate RHS of curve equation

func (*FP) Equals

func (F *FP) Equals(a *FP) bool

return TRUE if this==a

func (*FP) ToBytes

func (F *FP) ToBytes(b []byte)

func (*FP) ToString

func (F *FP) ToString() string