nim-libp2p-experimental/libp2p/crypto/ecnist.nim

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2019-02-19 22:11:59 +00:00
## Nim-Libp2p
## Copyright (c) 2018 Status Research & Development GmbH
## Licensed under either of
## * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE))
## * MIT license ([LICENSE-MIT](LICENSE-MIT))
## at your option.
## This file may not be copied, modified, or distributed except according to
## those terms.
import common
import nimcrypto/utils
import minasn1
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const
PubKey256Length* = 65
PubKey384Length* = 97
PubKey521Length* = 133
SecKey256Length* = 32
SecKey384Length* = 48
SecKey521Length* = 66
Sig256Length* = 64
Sig384Length* = 96
Sig521Length* = 132
type
EcPrivateKey* = ref object
buffer*: seq[byte]
key*: BrEcPrivateKey
EcPublicKey* = ref object
buffer*: seq[byte]
key*: BrEcPublicKey
EcKeyPair* = object
seckey*: EcPrivateKey
pubkey*: EcPublicKey
EcSignature* = ref object
buffer*: seq[byte]
curve*: cint
EcCurveKind* = enum
Secp256r1 = BR_EC_SECP256R1,
Secp384r1 = BR_EC_SECP384R1,
Secp521r1 = BR_EC_SECP521R1
EcPKI* = EcPrivateKey | EcPublicKey | EcSignature
EcError* = object of Exception
EcKeyIncorrectError* = object of EcError
EcRngError* = object of EcError
EcPublicKeyError* = object of EcError
EcSignatureError = object of EcError
const
EcSupportedCurvesCint* = {cint(Secp256r1), cint(Secp384r1), cint(Secp521r1)}
proc `-`(x: uint32): uint32 {.inline.} =
result = (0xFFFF_FFFF'u32 - x) + 1'u32
proc GT(x, y: uint32): uint32 {.inline.} =
var z = cast[uint32](y - x)
result = (z xor ((x xor y) and (x xor z))) shr 31
proc CMP(x, y: uint32): int32 {.inline.} =
cast[int32](GT(x, y)) or -(cast[int32](GT(y, x)))
proc EQ0(x: int32): uint32 {.inline.} =
var q = cast[uint32](x)
result = not(q or -q) shr 31
proc NEQ(x, y: uint32): uint32 {.inline.} =
var q = cast[uint32](x xor y)
result = ((q or -q) shr 31)
proc LT0(x: int32): uint32 {.inline.} =
result = cast[uint32](x) shr 31
proc checkScalar(scalar: openarray[byte], curve: cint): uint32 =
## Return ``1`` if all of the following hold:
## - len(``scalar``) <= ``orderlen``
## - ``scalar`` != 0
## - ``scalar`` is lower than the curve ``order``.
##
## Otherwise, return ``0``.
var impl = brEcGetDefault()
var orderlen = 0
var order = cast[ptr UncheckedArray[byte]](impl.order(curve, addr orderlen))
var z = 0'u32
var c = 0'i32
for u in scalar:
z = z or u
if len(scalar) == orderlen:
for i in 0..<len(scalar):
c = c or -(cast[int32](EQ0(c)) and CMP(scalar[i], order[i]))
else:
c = -1
result = NEQ(z, 0'u32) and LT0(c)
proc checkPublic(key: openarray[byte], curve: cint): uint32 =
## Return ``1`` if public key ``key`` is on curve.
var ckey = @key
var x = [0x00'u8, 0x01'u8]
var impl = brEcGetDefault()
var orderlen = 0
var order = impl.order(curve, addr orderlen)
result = impl.mul(cast[ptr cuchar](unsafeAddr ckey[0]), len(ckey),
cast[ptr cuchar](addr x[0]), len(x), curve)
proc getOffset(pubkey: EcPublicKey): int {.inline.} =
let o = cast[uint](pubkey.key.q) - cast[uint](unsafeAddr pubkey.buffer[0])
if o + cast[uint](pubkey.key.qlen) > uint(len(pubkey.buffer)):
result = -1
else:
result = cast[int](o)
proc getOffset(seckey: EcPrivateKey): int {.inline.} =
let o = cast[uint](seckey.key.x) - cast[uint](unsafeAddr seckey.buffer[0])
if o + cast[uint](seckey.key.xlen) > uint(len(seckey.buffer)):
result = -1
else:
result = cast[int](o)
template getSignatureLength*(curve: EcCurveKind): int =
case curve
of Secp256r1:
Sig256Length
of Secp384r1:
Sig384Length
of Secp521r1:
Sig521Length
template getPublicKeyLength*(curve: EcCurveKind): int =
case curve
of Secp256r1:
PubKey256Length
of Secp384r1:
PubKey384Length
of Secp521r1:
PubKey521Length
template getPrivateKeyLength*(curve: EcCurveKind): int =
case curve
of Secp256r1:
SecKey256Length
of Secp384r1:
SecKey384Length
of Secp521r1:
SecKey521Length
proc copy*[T: EcPKI](dst: var T, src: T): bool =
## Copy EC private key, public key or scalar ``src`` to ``dst``.
##
## Returns ``true`` on success, ``false`` otherwise.
dst = new T
when T is EcPrivateKey:
let length = src.key.xlen
if length > 0 and len(src.buffer) > 0:
let offset = getOffset(src)
if offset >= 0:
dst.buffer = src.buffer
dst.key.curve = src.key.curve
dst.key.xlen = length
dst.key.x = cast[ptr cuchar](addr dst.buffer[offset])
result = true
elif T is EcPublicKey:
let length = src.key.qlen
if length > 0 and len(src.buffer) > 0:
let offset = getOffset(src)
if offset >= 0:
dst.buffer = src.buffer
dst.key.curve = src.key.curve
dst.key.qlen = length
dst.key.q = cast[ptr cuchar](addr dst.buffer[offset])
result = true
else:
let length = len(src.buffer)
if length > 0:
dst.buffer = src.buffer
dst.curve = src.curve
result = true
proc copy*[T: EcPKI](src: T): T {.inline.} =
## Returns copy of EC private key, public key or scalar ``src``.
if not copy(result, src):
raise newException(EcKeyIncorrectError, "Incorrect key or signature")
proc clear*[T: EcPKI|EcKeyPair](pki: var T) =
## Wipe and clear EC private key, public key or scalar object.
when T is EcPrivateKey:
burnMem(pki.buffer)
pki.buffer.setLen(0)
pki.key.x = nil
pki.key.xlen = 0
pki.key.curve = 0
elif T is EcPublicKey:
burnMem(pki.buffer)
pki.buffer.setLen(0)
pki.key.q = nil
pki.key.qlen = 0
pki.key.curve = 0
elif T is EcSignature:
burnMem(pki.buffer)
pki.buffer.setLen(0)
pki.curve = 0
else:
burnMem(pki.seckey.buffer)
burnMem(pki.pubkey.buffer)
pki.seckey.buffer.setLen(0)
pki.pubkey.buffer.setLen(0)
pki.seckey.key.x = nil
pki.seckey.key.xlen = 0
pki.seckey.key.curve = 0
pki.pubkey.key.q = nil
pki.pubkey.key.qlen = 0
pki.pubkey.key.curve = 0
proc random*(t: typedesc[EcPrivateKey], kind: EcCurveKind): EcPrivateKey =
## Generate new random EC private key using BearSSL's HMAC-SHA256-DRBG
## algorithm.
##
## ``kind`` elliptic curve kind of your choice (secp256r1, secp384r1 or
## secp521r1).
var rng: BrHmacDrbgContext
var seeder = brPrngSeederSystem(nil)
brHmacDrbgInit(addr rng, addr sha256Vtable, nil, 0)
if seeder(addr rng.vtable) == 0:
raise newException(ValueError, "Could not seed RNG")
var ecimp = brEcGetDefault()
result = new EcPrivateKey
result.buffer = newSeq[byte](BR_EC_KBUF_PRIV_MAX_SIZE)
if brEcKeygen(addr rng.vtable, ecimp,
addr result.key, addr result.buffer[0],
cast[cint](kind)) == 0:
raise newException(ValueError, "Could not generate private key")
proc getKey*(seckey: EcPrivateKey): EcPublicKey =
## Calculate and return EC public key from private key ``seckey``.
var ecimp = brEcGetDefault()
if seckey.key.curve in EcSupportedCurvesCint:
var length = getPublicKeyLength(cast[EcCurveKind](seckey.key.curve))
result = new EcPublicKey
result.buffer = newSeq[byte](length)
if brEcComputePublicKey(ecimp, addr result.key,
addr result.buffer[0], unsafeAddr seckey.key) == 0:
raise newException(EcKeyIncorrectError, "Could not calculate public key")
else:
raise newException(EcKeyIncorrectError, "Incorrect private key")
proc random*(t: typedesc[EcKeyPair], kind: EcCurveKind): EcKeyPair {.inline.} =
## Generate new random EC private and public keypair using BearSSL's
## HMAC-SHA256-DRBG algorithm.
##
## ``kind`` elliptic curve kind of your choice (secp256r1, secp384r1 or
## secp521r1).
result.seckey = EcPrivateKey.random(kind)
result.pubkey = result.seckey.getKey()
proc `$`*(seckey: EcPrivateKey): string =
## Return string representation of EC private key.
if seckey.key.curve == 0 or seckey.key.xlen == 0 or len(seckey.buffer) == 0:
result = "Empty key"
else:
if seckey.key.curve notin EcSupportedCurvesCint:
result = "Unknown key"
else:
let offset = seckey.getOffset()
if offset < 0:
result = "Corrupted key"
else:
let e = offset + cast[int](seckey.key.xlen) - 1
result = toHex(seckey.buffer.toOpenArray(offset, e))
proc `$`*(pubkey: EcPublicKey): string =
## Return string representation of EC public key.
if pubkey.key.curve == 0 or pubkey.key.qlen == 0 or len(pubkey.buffer) == 0:
result = "Empty key"
else:
if pubkey.key.curve notin EcSupportedCurvesCint:
result = "Unknown key"
else:
let offset = pubkey.getOffset()
if offset < 0:
result = "Corrupted key"
else:
let e = offset + cast[int](pubkey.key.qlen) - 1
result = toHex(pubkey.buffer.toOpenArray(offset, e))
proc `$`*(sig: EcSignature): string =
## Return hexadecimal string representation of EC signature.
if sig.curve == 0 or len(sig.buffer) == 0:
result = "Empty signature"
else:
if sig.curve notin EcSupportedCurvesCint:
result = "Unknown signature"
else:
result = toHex(sig.buffer)
proc toBytes*(seckey: EcPrivateKey, data: var openarray[byte]): int =
## Serialize EC private key ``seckey`` to ASN.1 DER binary form and store it
## to ``data``.
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##
## Procedure returns number of bytes (octets) needed to store EC private key,
## or `0` if private key is not in supported curve.
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if seckey.key.curve in EcSupportedCurvesCint:
var offset, length: int
var pubkey = seckey.getKey()
var b = Asn1Buffer.init()
var p = Asn1Composite.init(Asn1Tag.Sequence)
var c0 = Asn1Composite.init(0)
var c1 = Asn1Composite.init(1)
if seckey.key.curve == BR_EC_SECP256R1:
c0.write(Asn1Tag.Oid, Asn1OidSecp256r1)
elif seckey.key.curve == BR_EC_SECP384R1:
c0.write(Asn1Tag.Oid, Asn1OidSecp384r1)
elif seckey.key.curve == BR_EC_SECP521R1:
c0.write(Asn1Tag.Oid, Asn1OidSecp521r1)
c0.finish()
offset = pubkey.getOffset()
length = pubkey.key.qlen
c1.write(Asn1Tag.BitString,
pubkey.buffer.toOpenArray(offset, offset + length - 1))
c1.finish()
offset = seckey.getOffset()
length = seckey.key.xlen
p.write(1'u64)
p.write(Asn1Tag.OctetString,
seckey.buffer.toOpenArray(offset, offset + length - 1))
p.write(c0)
p.write(c1)
p.finish()
b.write(p)
b.finish()
result = len(b)
if len(data) >= len(b):
copyMem(addr data[0], addr b.buffer[0], len(b))
proc toBytes*(pubkey: EcPublicKey, data: var openarray[byte]): int =
## Serialize EC public key ``pubkey`` to ASN.1 DER binary form and store it
## to ``data``.
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##
## Procedure returns number of bytes (octets) needed to store EC public key,
## or `0` if public key is not in supported curve.
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if pubkey.key.curve in EcSupportedCurvesCint:
var b = Asn1Buffer.init()
var p = Asn1Composite.init(Asn1Tag.Sequence)
var c = Asn1Composite.init(Asn1Tag.Sequence)
c.write(Asn1Tag.Oid, Asn1OidEcPublicKey)
if pubkey.key.curve == BR_EC_SECP256R1:
c.write(Asn1Tag.Oid, Asn1OidSecp256r1)
elif pubkey.key.curve == BR_EC_SECP384R1:
c.write(Asn1Tag.Oid, Asn1OidSecp384r1)
elif pubkey.key.curve == BR_EC_SECP521R1:
c.write(Asn1Tag.Oid, Asn1OidSecp521r1)
c.finish()
p.write(c)
let offset = getOffset(pubkey)
let length = pubkey.key.qlen
p.write(Asn1Tag.BitString,
pubkey.buffer.toOpenArray(offset, offset + length - 1))
p.finish()
b.write(p)
b.finish()
result = len(b)
if len(data) >= len(b):
copyMem(addr data[0], addr b.buffer[0], len(b))
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proc getBytes*(seckey: EcPrivateKey): seq[byte] =
## Serialize EC private key ``seckey`` to ASN.1 DER binary form and return it.
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if seckey.key.curve in EcSupportedCurvesCint:
result = newSeq[byte]()
let length = seckey.toBytes(result)
result.setLen(length)
discard seckey.toBytes(result)
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else:
raise newException(EcKeyIncorrectError, "Incorrect private key")
proc getBytes*(pubkey: EcPublicKey): seq[byte] =
## Serialize EC public key ``pubkey`` to ASN.1 DER binary form and return it.
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if pubkey.key.curve in EcSupportedCurvesCint:
result = newSeq[byte]()
let length = pubkey.toBytes(result)
result.setLen(length)
discard pubkey.toBytes(result)
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else:
raise newException(EcKeyIncorrectError, "Incorrect public key")
proc `==`*(pubkey1, pubkey2: EcPublicKey): bool =
## Returns ``true`` if both keys ``pubkey1`` and ``pubkey2`` are equal.
if pubkey1.key.curve != pubkey2.key.curve:
return false
if pubkey1.key.qlen != pubkey2.key.qlen:
return false
let op1 = pubkey1.getOffset()
let op2 = pubkey2.getOffset()
if op1 == -1 or op2 == -1:
return false
result = equalMem(unsafeAddr pubkey1.buffer[op1],
unsafeAddr pubkey2.buffer[op2], pubkey1.key.qlen)
proc `==`*(seckey1, seckey2: EcPrivateKey): bool =
## Returns ``true`` if both keys ``seckey1`` and ``seckey2`` are equal.
if seckey1.key.curve != seckey2.key.curve:
return false
if seckey1.key.xlen != seckey2.key.xlen:
return false
let op1 = seckey1.getOffset()
let op2 = seckey2.getOffset()
if op1 == -1 or op2 == -1:
return false
result = equalMem(unsafeAddr seckey1.buffer[op1],
unsafeAddr seckey2.buffer[op2], seckey1.key.xlen)
proc `==`*(sig1, sig2: EcSignature): bool =
## Return ``true`` if both signatures ``sig1`` and ``sig2`` are equal.
if sig1.curve != sig2.curve:
return false
result = (sig1.buffer == sig2.buffer)
proc init*(key: var EcPrivateKey, data: openarray[byte]): Asn1Status =
## Initialize EC `private key` or `scalar` ``key`` from ASN.1 DER binary
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## representation ``data``.
##
## Procedure returns ``Asn1Status``.
var raw, oid, field: Asn1Field
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var curve: cint
var ab = Asn1Buffer.init(data)
result = ab.read(field)
if result != Asn1Status.Success:
return
if field.kind != Asn1Tag.Sequence:
return Asn1Status.Incorrect
var ib = field.getBuffer()
result = ib.read(field)
if result != Asn1Status.Success:
return
if field.kind != Asn1Tag.Integer:
return Asn1Status.Incorrect
if field.vint != 1'u64:
return Asn1Status.Incorrect
result = ib.read(raw)
if result != Asn1Status.Success:
return
if raw.kind != Asn1Tag.OctetString:
return Asn1Status.Incorrect
result = ib.read(oid)
if result != Asn1Status.Success:
return
if oid.kind != Asn1Tag.Oid:
return Asn1Status.Incorrect
if oid == Asn1OidSecp256r1:
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curve = cast[cint](Secp256r1)
elif oid == Asn1OidSecp384r1:
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curve = cast[cint](Secp384r1)
elif oid == Asn1OidSecp521r1:
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curve = cast[cint](Secp521r1)
else:
return Asn1Status.Incorrect
if checkScalar(raw.toOpenArray(), curve) == 1'u32:
key = new EcPrivateKey
key.buffer = newSeq[byte](raw.length)
copyMem(addr key.buffer[0], addr raw.buffer[raw.offset], raw.length)
key.key.x = cast[ptr cuchar](addr key.buffer[0])
key.key.xlen = raw.length
key.key.curve = curve
result = Asn1Status.Success
else:
result = Asn1Status.Incorrect
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proc init*(pubkey: var EcPublicKey, data: openarray[byte]): Asn1Status =
## Initialize EC public key ``pubkey`` from ASN.1 DER binary representation
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## ``data``.
##
## Procedure returns ``Asn1Status``.
var raw, oid, field: Asn1Field
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var curve: cint
var ab = Asn1Buffer.init(data)
result = ab.read(field)
if result != Asn1Status.Success:
return
if field.kind != Asn1Tag.Sequence:
return Asn1Status.Incorrect
var ib = field.getBuffer()
result = ib.read(field)
if result != Asn1Status.Success:
return
if field.kind != Asn1Tag.Sequence:
return Asn1Status.Incorrect
var ob = field.getBuffer()
result = ob.read(oid)
if result != Asn1Status.Success:
return
if oid.kind != Asn1Tag.Oid:
return Asn1Status.Incorrect
if oid != Asn1OidEcPublicKey:
return Asn1Status.Incorrect
result = ob.read(oid)
if result != Asn1Status.Success:
return
if oid.kind != Asn1Tag.Oid:
return Asn1Status.Incorrect
if oid == Asn1OidSecp256r1:
curve = cast[cint](Secp256r1)
elif oid == Asn1OidSecp384r1:
curve = cast[cint](Secp384r1)
elif oid == Asn1OidSecp521r1:
curve = cast[cint](Secp521r1)
else:
return Asn1Status.Incorrect
result = ib.read(raw)
if result != Asn1Status.Success:
return
if raw.kind != Asn1Tag.BitString:
return Asn1Status.Incorrect
if checkPublic(raw.toOpenArray(), curve) != 0:
pubkey = new EcPublicKey
pubkey.buffer = newSeq[byte](raw.length)
copyMem(addr pubkey.buffer[0], addr raw.buffer[raw.offset], raw.length)
pubkey.key.q = cast[ptr cuchar](addr pubkey.buffer[0])
pubkey.key.qlen = raw.length
pubkey.key.curve = curve
result = Asn1Status.Success
else:
result = Asn1Status.Incorrect
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proc init*(sig: var EcSignature, data: openarray[byte]): bool =
## Initialize EC signature ``sig`` from raw binary representation ``data``.
##
## Length of ``data`` array must be ``Sig256Length``, ``Sig384Length``
## or ``Sig521Length``.
##
## Procedure returns ``true`` on success, ``false`` otherwise.
var curve: cint
if len(data) > 0:
if len(data) == Sig256Length:
curve = cast[cint](Secp256r1)
result = true
elif len(data) == Sig384Length:
curve = cast[cint](Secp384r1)
result = true
elif len(data) == Sig521Length:
curve = cast[cint](Secp521r1)
result = true
if result:
sig = new EcSignature
sig.curve = curve
sig.buffer = @data
result = true
proc init*[T: EcPKI](sospk: var T, data: string): bool {.inline.} =
## Initialize EC `private key`, `public key` or `scalar` ``sospk`` from
## hexadecimal string representation ``data``.
##
## Procedure returns ``true`` on success, ``false`` otherwise.
result = sospk.init(fromHex(data))
proc init*(t: typedesc[EcPrivateKey], data: openarray[byte]): EcPrivateKey =
## Initialize EC private key from ASN.1 DER binary representation ``data`` and
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## return constructed object.
let res = result.init(data)
if res != Asn1Status.Success:
raise newException(EcKeyIncorrectError,
"Incorrect private key (" & $res & ")")
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proc init*(t: typedesc[EcPublicKey], data: openarray[byte]): EcPublicKey =
## Initialize EC public key from ASN.1 DER binary representation ``data`` and
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## return constructed object.
let res = result.init(data)
if res != Asn1Status.Success:
raise newException(EcKeyIncorrectError,
"Incorrect public key (" & $res & ")")
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proc init*(t: typedesc[EcSignature], data: openarray[byte]): EcSignature =
## Initialize EC signature from raw binary representation ``data`` and
## return constructed object.
if not result.init(data):
raise newException(EcKeyIncorrectError, "Incorrect signature")
proc init*[T: EcPKI](t: typedesc[T], data: string): T {.inline.} =
## Initialize EC `private key`, `public key` or `scalar` from hexadecimal
## string representation ``data`` and return constructed object.
result = t.init(fromHex(data))
proc scalarMul*(pub: EcPublicKey, sec: EcPrivateKey): EcPublicKey =
## Return scalar multiplication of ``pub`` and ``sec``.
##
## Returns point in curve as ``pub * sec`` or ``nil`` otherwise.
var impl = brEcGetDefault()
if sec.key.curve in EcSupportedCurvesCint:
if pub.key.curve == sec.key.curve:
var key = new EcPublicKey
if key.copy(pub):
var slength = cint(0)
let poffset = key.getOffset()
let soffset = sec.getOffset()
if poffset >= 0 and soffset >= 0:
let res = impl.mul(cast[ptr cuchar](addr key.buffer[poffset]),
key.key.qlen,
cast[ptr cuchar](unsafeAddr sec.buffer[soffset]),
sec.key.xlen,
key.key.curve)
if res != 0:
result = key
proc sign*[T: byte|char](seckey: EcPrivateKey,
message: openarray[T]): EcSignature =
## Get ECDSA signature of data ``message`` using private key ``seckey``.
var hc: BrHashCompatContext
var hash: array[32, byte]
var impl = brEcGetDefault()
if len(message) > 0:
if seckey.key.curve in EcSupportedCurvesCint:
let length = getSignatureLength(cast[EcCurveKind](seckey.key.curve))
result = new EcSignature
result.curve = seckey.key.curve
result.buffer = newSeq[byte](length)
var kv = addr sha256Vtable
kv.init(addr hc.vtable)
kv.update(addr hc.vtable, unsafeAddr message[0], len(message))
kv.output(addr hc.vtable, addr hash[0])
let res = brEcdsaSignRaw(impl, kv, addr hash[0], addr seckey.key,
addr result.buffer[0])
if res != getSignatureLength(cast[EcCurveKind](result.curve)):
raise newException(EcSignatureError, "Could not make signature")
# Clear context with initial value
kv.init(addr hc.vtable)
else:
raise newException(EcKeyIncorrectError, "Incorrect private key")
else:
raise newException(EcSignatureError, "Empty message")
proc verify*[T: byte|char](sig: EcSignature, message: openarray[T],
pubkey: EcPublicKey): bool {.inline.} =
## Verify ECDSA signature ``sig`` using public key ``pubkey`` and data
## ``message``.
##
## Return ``true`` if message verification succeeded, ``false`` if
## verification failed.
var hc: BrHashCompatContext
var hash: array[32, byte]
var impl = brEcGetDefault()
if len(message) > 0:
if pubkey.key.curve in EcSupportedCurvesCint and
pubkey.key.curve == sig.curve:
var kv = addr sha256Vtable
kv.init(addr hc.vtable)
kv.update(addr hc.vtable, unsafeAddr message[0], len(message))
kv.output(addr hc.vtable, addr hash[0])
let res = brEcdsaVerifyRaw(impl, addr hash[0], 32, unsafeAddr pubkey.key,
addr sig.buffer[0], len(sig.buffer))
# Clear context with initial value
kv.init(addr hc.vtable)
result = (res == 1)
when isMainModule:
var buffer = newSeq[byte]()
var kp = EcKeyPair.random(Secp256r1)
var length: int
var serializedSK = kp.seckey.getBytes()
var serializedPK = kp.pubkey.getBytes()
echo toHex(serializedPK)
echo toHex(serializedSK)
var kp2 = EcPrivateKey.init(serializedSK)
echo toHex(kp2.getBytes())
var pk2 = EcPublicKey.init(serializedPK)
echo repr pk2
echo toHex(pk2.getBytes())