bn254

package
v0.0.0-...-ab467c6 Latest Latest
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 Go to latest Published: Mar 2, 2022 License: Apache-2.0 Imports: 3 Imported by: 0

Documentation

Index

Constants

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const AESKEY int = 16
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const ALLOW_ALT_COMPRESS bool = false
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const ATE_BITS int = 66
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const BAD_PARAMS int = -11
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const BAD_PIN int = -19
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const BASEBITS uint = 56
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const BFS int = int(MODBYTES)
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const BGS int = int(MODBYTES)
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const BIGBITS int = int(MODBYTES * 8)
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const BIG_ENDIAN_SIGN bool = false
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const BLS12 int = 2
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const BLS24 int = 3
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const BLS48 int = 4
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const BLS_FAIL int = -1
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const BLS_OK int = 0
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const BN int = 1
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const CHUNK int = 64 /* Set word size */
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const CURVETYPE int = WEIERSTRASS
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const CURVE_A int = 0
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const CURVE_B_I int = 2
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const CURVE_Cof_I int = 1
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const CURVE_PAIRING_TYPE int = BN
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const DNLEN int = 2 * NLEN
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const D_TYPE int = 0

Pairing Twist type

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const EDWARDS int = 1
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const EFS int = int(MODBYTES)

const INVALID int = -4

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const EGS int = int(MODBYTES)
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const ERROR int = -3
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const FEXCESS int32 = ((int32(1) << 26) - 1)
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const FP_DENSE int = 5
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const FP_ONE int = 1
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const FP_SPARSE int = 4
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const FP_SPARSER int = 3
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const FP_SPARSEST int = 2
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const FP_ZERO int = 0

Sparsity

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const G2_TABLE int = 71
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const GENERALISED_MERSENNE int = 3
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const HASH_TYPE int = 32
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const HBITS uint = (BASEBITS / 2)
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const HTC_ISO int = 0
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const HTC_ISO_G2 int = 0
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const INVALID_POINT int = -14
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const INVALID_PUBLIC_KEY int = -2
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const MAXPIN int32 = 10000 /* PIN less than this */
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const MFS int = int(MODBYTES)

import "fmt"

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const MGS int = int(MODBYTES)
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const MODBITS uint = 254 /* Number of bits in Modulus */

Modulus details

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const MODBYTES uint = 32

BIG length in bytes and number base

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const MODTYPE int = NOT_SPECIAL //NOT_SPECIAL
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const MONTGOMERY int = 2
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const MONTGOMERY_FRIENDLY int = 2
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const M_TYPE int = 1
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const NEGATIVEX int = 1
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const NEGATOWER int = 0
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const NEXCESS int = (1 << (uint(CHUNK) - BASEBITS - 1))
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const NLEN int = int((1 + ((8*MODBYTES - 1) / BASEBITS)))

BIG lengths and Masks

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const NOT int = 0

Pairing Friendly?

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const NOT_SPECIAL int = 0

Modulus types

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const PBLEN int32 = 14 /* Number of bits in PIN */
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const PM1D2 uint = 1 /* Modulus mod 8 */
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const POSITIVEX int = 0

Pairing x parameter sign

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const POSITOWER int = 1
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const PSEUDO_MERSENNE int = 1
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const QNRI int = 0 // Fp2 QNR
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const RIADZ int = -1 /* hash-to-point Z */
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const RIADZG2A int = -1 /* G2 hash-to-point Z */
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const RIADZG2B int = 0 /* G2 hash-to-point Z */
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const SEXTIC_TWIST int = D_TYPE
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const SIGN_OF_X int = NEGATIVEX
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const TBITS uint = MODBITS % BASEBITS // Number of active bits in top word
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const TOWER int = NEGATOWER // Tower type
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const USE_GLV bool = true
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const USE_GS_G2 bool = true
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const USE_GS_GT bool = true
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const WEIERSTRASS int = 0

Curve types

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const WRONG_ORDER int = -18

Variables

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var CRu = [...]Chunk{0x80000000000007, 0x6CD, 0x40000000024909, 0x49B362, 0x0}
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var CURVE_B = [...]Chunk{0x2, 0x0, 0x0, 0x0, 0x0}
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var CURVE_BB = [4][4][5]Chunk{{{0x8000000000000D, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x8000000000000C, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x8000000000000C, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x2, 0x81, 0x0, 0x0, 0x0}}, {{0x1, 0x81, 0x0, 0x0, 0x0}, {0x8000000000000C, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x8000000000000D, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x8000000000000C, 0x80000000001060, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}}, {{0x2, 0x81, 0x0, 0x0, 0x0}, {0x1, 0x81, 0x0, 0x0, 0x0}, {0x1, 0x81, 0x0, 0x0, 0x0}, {0x1, 0x81, 0x0, 0x0, 0x0}}, {{0x80000000000002, 0x40, 0x0, 0x0, 0x0}, {0x2, 0x102, 0x0, 0x0, 0x0}, {0xA, 0x80000000001020, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}, {0x80000000000002, 0x40, 0x0, 0x0, 0x0}}}
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var CURVE_Bnx = [...]Chunk{0x80000000000001, 0x40, 0x0, 0x0, 0x0}
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var CURVE_Cof = [...]Chunk{0x1, 0x0, 0x0, 0x0, 0x0}
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var CURVE_Gx = [...]Chunk{0x12, 0x13A7, 0x80000000086121, 0x40000001BA344D, 0x25236482}
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var CURVE_Gy = [...]Chunk{0x1, 0x0, 0x0, 0x0, 0x0}
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var CURVE_HTPC = [...]Chunk{0x1, 0x0, 0x0, 0x0, 0x0}
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var CURVE_Order = [...]Chunk{0xD, 0x800000000010A1, 0x8000000007FF9F, 0x40000001BA344D, 0x25236482}
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var CURVE_Pxa = [...]Chunk{0xEE4224C803FB2B, 0x8BBB4898BF0D91, 0x7E8C61EDB6A464, 0x519EB62FEB8D8C, 0x61A10BB}
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var CURVE_Pxb = [...]Chunk{0x8C34C1E7D54CF3, 0x746BAE3784B70D, 0x8C5982AA5B1F4D, 0xBA737833310AA7, 0x516AAF9}
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var CURVE_Pya = [...]Chunk{0xF0E07891CD2B9A, 0xAE6BDBE09BD19, 0x96698C822329BD, 0x6BAF93439A90E0, 0x21897A0}
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var CURVE_Pyb = [...]Chunk{0x2D1AEC6B3ACE9B, 0x6FFD739C9578A, 0x56F5F38D37B090, 0x7C8B15268F6D44, 0xEBB2B0E}
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var CURVE_SB = [2][2][5]Chunk{{{0x4, 0x80000000000285, 0x6181, 0x0, 0x0}, {0x1, 0x81, 0x0, 0x0, 0x0}}, {{0x1, 0x81, 0x0, 0x0, 0x0}, {0xA, 0xE9D, 0x80000000079E1E, 0x40000001BA344D, 0x25236482}}}
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var CURVE_W = [2][5]Chunk{{0x3, 0x80000000000204, 0x6181, 0x0, 0x0}, {0x1, 0x81, 0x0, 0x0, 0x0}}
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var CURVE_WB = [4][5]Chunk{{0x80000000000000, 0x80000000000040, 0x2080, 0x0, 0x0}, {0x80000000000005, 0x54A, 0x8000000001C707, 0x312241, 0x0}, {0x80000000000003, 0x800000000002C5, 0xC000000000E383, 0x189120, 0x0}, {0x80000000000001, 0x800000000000C1, 0x2080, 0x0, 0x0}}
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var Fra = [...]Chunk{0x7DE6C06F2A6DE9, 0x74924D3F77C2E1, 0x50A846953F8509, 0x212E7C8CB6499B, 0x1B377619}
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var Frb = [...]Chunk{0x82193F90D5922A, 0x8B6DB2C08850C5, 0x2F57B96AC8DC17, 0x1ED1837503EAB2, 0x9EBEE69}
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var G2_TAB []*FP4
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var Modulus = [...]Chunk{0x13, 0x13A7, 0x80000000086121, 0x40000001BA344D, 0x25236482}

Base Bits= 56

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var R2modp = [...]Chunk{0x2F2A96FF5E7E39, 0x64E8642B96F13C, 0x9926F7B00C7146, 0x8321E7B4DACD24, 0x1D127A2E}
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var ROI = [...]Chunk{0x12, 0x13A7, 0x80000000086121, 0x40000001BA344D, 0x25236482}
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var SQRTm3 = [...]Chunk{0x4, 0x60C, 0x3CF0F, 0x4000000126CD89, 0x25236482}

Functions

func Another 

func Another(r []*FP12, P1 *ECP2, Q1 *ECP)

Accumulate another set of line functions for n-pairing

func Another_pc 

func Another_pc(r []*FP12, T []*FP4, QV *ECP)

Accumulate another set of line functions for n-pairing, assuming precomputation on G2

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 Core_Sign 

func Core_Sign(SIG []byte, M []byte, S []byte) int

func Core_Verify 

func Core_Verify(SIG []byte, M []byte, W []byte) int

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 G1member 

func G1member(P *ECP) bool

test G1 group membership

func G2member 

func G2member(P *ECP2) bool

test G2 group membership

func GTcyclotomic 

func GTcyclotomic(m *FP12) bool

Check that m is in cyclotomic sub-group Check that m!=1, conj(m)*m==1, and m.m^{p^4}=m^{p^2}

func GTmember 

func GTmember(m *FP12) bool

test for full GT membership

func Init 

func Init() int

func KeyPairGenerate 

func KeyPairGenerate(IKM []byte, S []byte, W []byte) int

generate key pair, private key S, public key W

func KeySchedule 

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

func MPIN_CLIENT_1 

func MPIN_CLIENT_1(CID []byte, rng *core.RAND, X []byte, pin int, TOKEN []byte, SEC []byte, xID []byte) int

Implement step 1 on client side of MPin protocol

func MPIN_CLIENT_2 

func MPIN_CLIENT_2(X []byte, Y []byte, SEC []byte) int

Implement step 2 on client side of MPin protocol

func MPIN_ENCODE_TO_CURVE 

func MPIN_ENCODE_TO_CURVE(DST []byte, ID []byte, HCID []byte)

func MPIN_EXTRACT_PIN 

func MPIN_EXTRACT_PIN(CID []byte, pin int, TOKEN []byte) int

func MPIN_GET_CLIENT_SECRET 

func MPIN_GET_CLIENT_SECRET(S []byte, IDHTC []byte, CST []byte) int

func MPIN_GET_SERVER_SECRET 

func MPIN_GET_SERVER_SECRET(S []byte, SST []byte) int

Extract Server Secret SST=S*Q where Q is fixed generator in G2 and S is master secret

func MPIN_HASH_ID 

func MPIN_HASH_ID(sha int, ID []byte) []byte

func MPIN_RANDOM_GENERATE 

func MPIN_RANDOM_GENERATE(rng *core.RAND, S []byte) int

create random secret S

func MPIN_SERVER 

func MPIN_SERVER(HID []byte, Y []byte, SST []byte, xID []byte, mSEC []byte) int

Implement step 2 of MPin protocol on server side

func RFC7748 

func RFC7748(r *BIG)

Transform a point multiplier to RFC7748 form

Types

type BIG 

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

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 = 0x435E50D79435E5
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 G1mul 

func G1mul(P *ECP, e *BIG) *ECP

Multiply P by e in group G1

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 ECP2 

type ECP2 struct {
	// contains filtered or unexported fields
}

func ECP2_fromBytes 

func ECP2_fromBytes(b []byte) *ECP2

convert from byte array to point

func ECP2_generator 

func ECP2_generator() *ECP2

func ECP2_hap2point 

func ECP2_hap2point(h *BIG) *ECP2

Hunt and Peck a BIG to a curve point

func ECP2_map2point 

func ECP2_map2point(H *FP2) *ECP2

Constant time Map to Point

func ECP2_mapit 

func ECP2_mapit(h []byte) *ECP2

Map octet string to curve point

func G2mul 

func G2mul(P *ECP2, e *BIG) *ECP2

Multiply P by e in group G2

func NewECP2 

func NewECP2() *ECP2

func NewECP2fp2 

func NewECP2fp2(ix *FP2, s int) *ECP2

construct this from x - but set to O if not on curve

func NewECP2fp2s 

func NewECP2fp2s(ix *FP2, iy *FP2) *ECP2

construct this from (x,y) - but set to O if not on curve

func (*ECP2) Add 

func (E *ECP2) Add(Q *ECP2) int

this+=Q - return 0 for add, 1 for double, -1 for O

func (*ECP2) Affine 

func (E *ECP2) Affine()

set to Affine - (x,y,z) to (x,y)

func (*ECP2) Cfp 

func (E *ECP2) Cfp()

clear cofactor

func (*ECP2) Copy 

func (E *ECP2) Copy(P *ECP2)

copy this=P

func (*ECP2) Equals 

func (E *ECP2) Equals(Q *ECP2) bool

Test if P == Q

func (*ECP2) GetX 

func (E *ECP2) GetX() *FP2

extract affine x as FP2

func (*ECP2) GetY 

func (E *ECP2) GetY() *FP2

extract affine y as FP2

func (*ECP2) Is_infinity 

func (E *ECP2) Is_infinity() bool

Test this=O?

func (*ECP2) Mul 

func (E *ECP2) Mul(e *BIG) *ECP2

Public version

func (*ECP2) Sub 

func (E *ECP2) Sub(Q *ECP2) int

set this-=Q

func (*ECP2) ToBytes 

func (E *ECP2) ToBytes(b []byte, compress bool)

convert to byte array

func (*ECP2) ToString 

func (E *ECP2) ToString() string

convert this 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

type FP12 

type FP12 struct {
	// contains filtered or unexported fields
}

func Ate 

func Ate(P1 *ECP2, Q1 *ECP) *FP12

Optimal R-ate pairing

func Ate2 

func Ate2(P1 *ECP2, Q1 *ECP, R1 *ECP2, S1 *ECP) *FP12

Optimal R-ate double pairing e(P,Q).e(R,S)

func FP12_fromBytes 

func FP12_fromBytes(w []byte) *FP12

convert from byte array to FP12

func Fexp 

func Fexp(m *FP12) *FP12

final exponentiation - keep separate for multi-pairings and to avoid thrashing stack

func GTpow 

func GTpow(d *FP12, e *BIG) *FP12

f=f^e Note that this method requires a lot of RAM! Better to use compressed XTR method, see FP4.java

func Initmp 

func Initmp() []*FP12

prepare for multi-pairing

func Miller 

func Miller(r []*FP12) *FP12

basic Miller loop

func NewFP12 

func NewFP12() *FP12

func NewFP12copy 

func NewFP12copy(x *FP12) *FP12

func NewFP12fp4 

func NewFP12fp4(d *FP4) *FP12

Constructors

func NewFP12fp4s 

func NewFP12fp4s(d *FP4, e *FP4, f *FP4) *FP12

func NewFP12int 

func NewFP12int(d int) *FP12

func (*FP12) Compow 

func (F *FP12) Compow(e *BIG, r *BIG) *FP4

Fast compressed FP4 power of unitary FP12

func (*FP12) Copy 

func (F *FP12) Copy(x *FP12)

copy this=x

func (*FP12) Equals 

func (F *FP12) Equals(x *FP12) bool

return 1 if x==y, else 0

func (*FP12) Inverse 

func (F *FP12) Inverse()

this=1/this

func (*FP12) Isunity 

func (F *FP12) Isunity() bool

test x==1 ?

func (*FP12) Mul 

func (F *FP12) Mul(y *FP12)

FP12 full multiplication this=this*y

func (*FP12) Pow 

func (F *FP12) Pow(e *BIG) *FP12

this=this^e

func (*FP12) ToBytes 

func (F *FP12) ToBytes(w []byte)

convert this to byte array

func (*FP12) ToString 

func (F *FP12) ToString() string

convert to hex string

type FP2 

type FP2 struct {
	// contains filtered or unexported fields
}

func FP2_fromBytes 

func FP2_fromBytes(bf []byte) *FP2

func NewFP2 

func NewFP2() *FP2

func NewFP2big 

func NewFP2big(c *BIG) *FP2

func NewFP2bigs 

func NewFP2bigs(c *BIG, d *BIG) *FP2

func NewFP2copy 

func NewFP2copy(x *FP2) *FP2

func NewFP2fp 

func NewFP2fp(c *FP) *FP2

func NewFP2fps 

func NewFP2fps(c *FP, d *FP) *FP2

func NewFP2int 

func NewFP2int(a int) *FP2

Constructors

func NewFP2ints 

func NewFP2ints(a int, b int) *FP2

func NewFP2rand 

func NewFP2rand(rng *core.RAND) *FP2

func RHS2 

func RHS2(x *FP2) *FP2

Calculate RHS of twisted curve equation x^3+B/i

func (*FP2) Equals 

func (F *FP2) Equals(x *FP2) bool

test this=x

func (*FP2) GetA 

func (F *FP2) GetA() *BIG

extract a

func (*FP2) GetB 

func (F *FP2) GetB() *BIG

extract b

func (*FP2) ToBytes 

func (F *FP2) ToBytes(bf []byte)

func (*FP2) ToString 

func (F *FP2) ToString() string

output to hex string

type FP4 

type FP4 struct {
	// contains filtered or unexported fields
}

func FP4_fromBytes 

func FP4_fromBytes(bf []byte) *FP4

func NewFP4 

func NewFP4() *FP4

func NewFP4copy 

func NewFP4copy(x *FP4) *FP4

func NewFP4fp 

func NewFP4fp(c *FP) *FP4

func NewFP4fp2 

func NewFP4fp2(c *FP2) *FP4

func NewFP4fp2s 

func NewFP4fp2s(c *FP2, d *FP2) *FP4

func NewFP4int 

func NewFP4int(a int) *FP4

Constructors

func NewFP4ints 

func NewFP4ints(a int, b int) *FP4

Constructors

func NewFP4rand 

func NewFP4rand(rng *core.RAND) *FP4

func (*FP4) Equals 

func (F *FP4) Equals(x *FP4) bool

test this=x?

func (*FP4) ToBytes 

func (F *FP4) ToBytes(bf []byte)

Source Files

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