nim-libp2p/libp2p/crypto/rsa.nim

## 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.

## This module implements constant-time RSA PKCS#1.5 DSA.
##
## This module uses unmodified parts of code from
## BearSSL library <https://bearssl.org/>
## Copyright(C) 2018 Thomas Pornin <pornin@bolet.org>.
import nimcrypto/utils
import bearssl
import minasn1
export Asn1Status

const
  DefaultPublicExponent* = 3'u32
    ## Default value for RSA public exponent.
  MinKeySize* = 512
    ## Minimal allowed RSA key size in bits.
  DefaultKeySize* = 2048
    ## Default RSA key size in bits.

  RsaOidSha1* = [
    0x05'u8, 0x2B'u8, 0x0E'u8, 0x03'u8, 0x02'u8, 0x1A'u8
  ]
    ## RSA PKCS#1.5 SHA-1 hash object identifier.
  RsaOidSha224* = [
    0x09'u8, 0x60'u8, 0x86'u8, 0x48'u8, 0x01'u8, 0x65'u8, 0x03'u8, 0x04'u8,
    0x02'u8, 0x04'u8
  ]
    ## RSA PKCS#1.5 SHA-224 hash object identifier.
  RsaOidSha256* = [
    0x09'u8, 0x60'u8, 0x86'u8, 0x48'u8, 0x01'u8, 0x65'u8, 0x03'u8, 0x04'u8,
    0x02'u8, 0x01'u8
  ]
    ## RSA PKCS#1.5 SHA-256 hash object identifier.
  RsaOidSha384* = [
    0x09'u8, 0x60'u8, 0x86'u8, 0x48'u8, 0x01'u8, 0x65'u8, 0x03'u8, 0x04'u8,
    0x02'u8, 0x02'u8
  ]
    ## RSA PKCS#1.5 SHA-384 hash object identifier.
  RsaOidSha512* = [
    0x09'u8, 0x60'u8, 0x86'u8, 0x48'u8, 0x01'u8, 0x65'u8, 0x03'u8, 0x04'u8,
    0x02'u8, 0x03'u8
  ]
    ## RSA PKCS#1.5 SHA-512 hash object identifier.

type
  RsaPrivateKey* = ref object
    buffer*: seq[byte]
    seck*: BrRsaPrivateKey
    pubk*: BrRsaPublicKey
    pexp*: ptr cuchar
    pexplen*: int

  RsaPublicKey* = ref object
    buffer*: seq[byte]
    key*: BrRsaPublicKey

  RsaKeyPair* = RsaPrivateKey

  RsaSignature* = ref object
    buffer*: seq[byte]

  RsaPKI* = RsaPrivateKey | RsaPublicKey | RsaSignature
  RsaKP* = RsaPrivateKey | RsaKeyPair

  RsaError* = object of CatchableError
  RsaRngError* = object of RsaError
  RsaGenError* = object of RsaError
  RsaKeyIncorrectError* = object of RsaError
  RsaSignatureError* = object of RsaError

template getStart(bs, os, ls: untyped): untyped =
  let p = cast[uint](os)
  let s = cast[uint](unsafeAddr bs[0])
  var so = 0
  if p >= s:
    so = cast[int](p - s)
  so

template getFinish(bs, os, ls: untyped): untyped =
  let p = cast[uint](os)
  let s = cast[uint](unsafeAddr bs[0])
  var eo = -1
  if p >= s:
    let so = cast[int](p - s)
    if so + ls <= len(bs):
      eo = so + ls - 1
  eo

template getArray*(bs, os, ls: untyped): untyped =
  toOpenArray(bs, getStart(bs, os, ls), getFinish(bs, os, ls))

template trimZeroes(b: seq[byte], pt, ptlen: untyped) =
  var length = ptlen
  for i in 0..<length:
    if pt[] != cast[cuchar](0x00'u8):
      break
    pt = cast[ptr cuchar](cast[uint](pt) + 1)
    ptlen -= 1

proc random*[T: RsaKP](t: typedesc[T], bits = DefaultKeySize,
                       pubexp = DefaultPublicExponent): T =
  ## Generate new random RSA private key using BearSSL's HMAC-SHA256-DRBG
  ## algorithm.
  ##
  ## ``bits`` number of bits in RSA key, must be in
  ## range [512, 4096] (default = 2048).
  ##
  ## ``pubexp`` is RSA public exponent, which must be prime (default = 3).
  var rng: BrHmacDrbgContext
  var keygen: BrRsaKeygen
  var seeder = brPrngSeederSystem(nil)
  brHmacDrbgInit(addr rng, addr sha256Vtable, nil, 0)
  if seeder(addr rng.vtable) == 0:
    raise newException(RsaRngError, "Could not seed RNG")
  keygen = brRsaKeygenGetDefault()

  let length = brRsaPrivateKeyBufferSize(bits) +
               brRsaPublicKeyBufferSize(bits) +
               ((bits + 7) shr 3)
  let sko = 0
  let pko = brRsaPrivateKeyBufferSize(bits)
  let eko = pko + brRsaPublicKeyBufferSize(bits)

  when T is RsaKeyPair:
    result = new RsaKeyPair
  else:
    result = new RsaPrivateKey

  result.buffer = newSeq[byte](length)
  if keygen(addr rng.vtable,
            addr result.seck, addr result.buffer[sko],
            addr result.pubk, addr result.buffer[pko],
            cuint(bits), pubexp) == 0:
    raise newException(RsaGenError, "Could not create private key")

  let compute = brRsaComputePrivexpGetDefault()
  let res = compute(addr result.buffer[eko], addr result.seck, pubexp)
  if res == 0:
    raise newException(RsaGenError, "Could not create private key")

  result.pexp = cast[ptr cuchar](addr result.buffer[eko])
  result.pexplen = res

  trimZeroes(result.buffer, result.seck.p, result.seck.plen)
  trimZeroes(result.buffer, result.seck.q, result.seck.qlen)
  trimZeroes(result.buffer, result.seck.dp, result.seck.dplen)
  trimZeroes(result.buffer, result.seck.dq, result.seck.dqlen)
  trimZeroes(result.buffer, result.seck.iq, result.seck.iqlen)
  trimZeroes(result.buffer, result.pubk.n, result.pubk.nlen)
  trimZeroes(result.buffer, result.pubk.e, result.pubk.elen)
  trimZeroes(result.buffer, result.pexp, result.pexplen)

proc copy*[T: RsaPKI](key: T): T =
  ## Create copy of RSA private key, public key or signature.
  doAssert(not isNil(key))
  when T is RsaPrivateKey:
    if len(key.buffer) > 0:
      let length = key.seck.plen + key.seck.qlen + key.seck.dplen +
                   key.seck.dqlen + key.seck.iqlen + key.pubk.nlen +
                   key.pubk.elen + key.pexplen
      result = new RsaPrivateKey
      result.buffer = newSeq[byte](length)
      let po = 0
      let qo = po + key.seck.plen
      let dpo = qo + key.seck.qlen
      let dqo = dpo + key.seck.dplen
      let iqo = dqo + key.seck.dqlen
      let no = iqo + key.seck.iqlen
      let eo = no + key.pubk.nlen
      let peo = eo + key.pubk.elen
      copyMem(addr result.buffer[po], key.seck.p, key.seck.plen)
      copyMem(addr result.buffer[qo], key.seck.q, key.seck.qlen)
      copyMem(addr result.buffer[dpo], key.seck.dp, key.seck.dplen)
      copyMem(addr result.buffer[dqo], key.seck.dq, key.seck.dqlen)
      copyMem(addr result.buffer[iqo], key.seck.iq, key.seck.iqlen)
      copyMem(addr result.buffer[no], key.pubk.n, key.pubk.nlen)
      copyMem(addr result.buffer[eo], key.pubk.e, key.pubk.elen)
      copyMem(addr result.buffer[peo], key.pexp, key.pexplen)
      result.seck.p = cast[ptr cuchar](addr result.buffer[po])
      result.seck.q = cast[ptr cuchar](addr result.buffer[qo])
      result.seck.dp = cast[ptr cuchar](addr result.buffer[dpo])
      result.seck.dq = cast[ptr cuchar](addr result.buffer[dqo])
      result.seck.iq = cast[ptr cuchar](addr result.buffer[iqo])
      result.pubk.n = cast[ptr cuchar](addr result.buffer[no])
      result.pubk.e = cast[ptr cuchar](addr result.buffer[eo])
      result.pexp = cast[ptr cuchar](addr result.buffer[peo])
      result.seck.plen = key.seck.plen
      result.seck.qlen = key.seck.qlen
      result.seck.dplen = key.seck.dplen
      result.seck.dqlen = key.seck.dqlen
      result.seck.iqlen = key.seck.iqlen
      result.pubk.nlen = key.pubk.nlen
      result.pubk.elen = key.pubk.elen
      result.pexplen = key.pexplen
      result.seck.nBitlen = key.seck.nBitlen
  elif T is RsaPublicKey:
    if len(key.buffer) > 0:
      let length = key.key.nlen + key.key.elen
      result = new RsaPublicKey
      result.buffer = newSeq[byte](length)
      let no = 0
      let eo = no + key.key.nlen
      copyMem(addr result.buffer[no], key.key.n, key.key.nlen)
      copyMem(addr result.buffer[eo], key.key.e, key.key.elen)
      result.key.n = cast[ptr cuchar](addr result.buffer[no])
      result.key.e = cast[ptr cuchar](addr result.buffer[eo])
      result.key.nlen = key.key.nlen
      result.key.elen = key.key.elen
  elif T is RsaSignature:
    if len(key.buffer) > 0:
      result = new RsaSignature
      result.buffer = key.buffer

proc getKey*(key: RsaPrivateKey): RsaPublicKey =
  ## Get RSA public key from RSA private key.
  doAssert(not isNil(key))
  let length = key.pubk.nlen + key.pubk.elen
  result = new RsaPublicKey
  result.buffer = newSeq[byte](length)
  result.key.n = cast[ptr cuchar](addr result.buffer[0])
  result.key.e = cast[ptr cuchar](addr result.buffer[key.pubk.nlen])
  copyMem(addr result.buffer[0], cast[pointer](key.pubk.n), key.pubk.nlen)
  copyMem(addr result.buffer[key.pubk.nlen], cast[pointer](key.pubk.e),
          key.pubk.elen)
  result.key.nlen = key.pubk.nlen
  result.key.elen = key.pubk.elen

proc seckey*(pair: RsaKeyPair): RsaPrivateKey {.inline.} =
  ## Get RSA private key from pair ``pair``.
  result = cast[RsaPrivateKey](pair).copy()

proc pubkey*(pair: RsaKeyPair): RsaPublicKey {.inline.} =
  ## Get RSA public key from pair ``pair``.
  result = cast[RsaPrivateKey](pair).getKey()

proc clear*[T: RsaPKI|RsaKeyPair](pki: var T) =
  ## Wipe and clear EC private key, public key or scalar object.
  doAssert(not isNil(pki))
  when T is RsaPrivateKey:
    burnMem(pki.buffer)
    pki.buffer.setLen(0)
    pki.seckey.p = nil
    pki.seckey.q = nil
    pki.seckey.dp = nil
    pki.seckey.dq = nil
    pki.seckey.iq = nil
    pki.seckey.plen = 0
    pki.seckey.qlen = 0
    pki.seckey.dplen = 0
    pki.seckey.dqlen = 0
    pki.seckey.iqlen = 0
    pki.seckey.nBitlen = 0
    pki.pubkey.n = nil
    pki.pubkey.e = nil
    pki.pubkey.nlen = 0
    pki.pubkey.elen = 0
  elif T is RsaPublicKey:
    burnMem(pki.buffer)
    pki.buffer.setLen(0)
    pki.key.n = nil
    pki.key.e = nil
    pki.key.nlen = 0
    pki.key.elen = 0
  elif T is RsaSignature:
    burnMem(pki.buffer)
    pki.buffer.setLen(0)

proc toBytes*(key: RsaPrivateKey, data: var openarray[byte]): int =
  ## Serialize RSA private key ``key`` to ASN.1 DER binary form and store it
  ## to ``data``.
  ##
  ## Procedure returns number of bytes (octets) needed to store RSA private key,
  ## or `0` if private key is is incorrect.
  doAssert(not isNil(key))
  if len(key.buffer) > 0:
    var b = Asn1Buffer.init()
    var p = Asn1Composite.init(Asn1Tag.Sequence)
    p.write(0'u64)
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.pubk.n,
                                      key.pubk.nlen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.pubk.e,
                                      key.pubk.elen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.pexp, key.pexplen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.seck.p,
                                      key.seck.plen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.seck.q,
                                      key.seck.qlen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.seck.dp,
                                      key.seck.dplen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.seck.dq,
                                      key.seck.dqlen))
    p.write(Asn1Tag.Integer, getArray(key.buffer, key.seck.iq,
                                      key.seck.iqlen))
    p.finish()
    b.write(p)
    b.finish()
    result = len(b)
    if len(data) >= result:
      copyMem(addr data[0], addr b.buffer[0], result)

proc toBytes*(key: RsaPublicKey, data: var openarray[byte]): int =
  ## Serialize RSA public key ``key`` to ASN.1 DER binary form and store it
  ## to ``data``.
  ##
  ## Procedure returns number of bytes (octets) needed to store RSA public key,
  ## or `0` if public key is incorrect.
  doAssert(not isNil(key))
  if len(key.buffer) > 0:
    var b = Asn1Buffer.init()
    var p = Asn1Composite.init(Asn1Tag.Sequence)
    var c0 = Asn1Composite.init(Asn1Tag.Sequence)
    var c1 = Asn1Composite.init(Asn1Tag.BitString)
    var c10 = Asn1Composite.init(Asn1Tag.Sequence)
    c0.write(Asn1Tag.Oid, Asn1OidRsaEncryption)
    c0.write(Asn1Tag.Null)
    c0.finish()
    c10.write(Asn1Tag.Integer, getArray(key.buffer, key.key.n, key.key.nlen))
    c10.write(Asn1Tag.Integer, getArray(key.buffer, key.key.e, key.key.elen))
    c10.finish()
    c1.write(c10)
    c1.finish()
    p.write(c0)
    p.write(c1)
    p.finish()
    b.write(p)
    b.finish()
    result = len(b)
    if len(data) >= result:
      copyMem(addr data[0], addr b.buffer[0], result)

proc toBytes*(sig: RsaSignature, data: var openarray[byte]): int =
  ## Serialize RSA signature ``sig`` to raw binary form and store it
  ## to ``data``.
  ##
  ## Procedure returns number of bytes (octets) needed to store RSA public key,
  ## or `0` if public key is incorrect.
  doAssert(not isNil(sig))
  result = len(sig.buffer)
  if len(data) >= result:
    copyMem(addr data[0], addr sig.buffer[0], result)

proc getBytes*(key: RsaPrivateKey): seq[byte] =
  ## Serialize RSA private key ``key`` to ASN.1 DER binary form and
  ## return it.
  doAssert(not isNil(key))
  result = newSeq[byte](4096)
  let length = key.toBytes(result)
  if length > 0:
    result.setLen(length)
  else:
    raise newException(RsaKeyIncorrectError, "Incorrect private key")

proc getBytes*(key: RsaPublicKey): seq[byte] =
  ## Serialize RSA public key ``key`` to ASN.1 DER binary form and
  ## return it.
  doAssert(not isNil(key))
  result = newSeq[byte](4096)
  let length = key.toBytes(result)
  if length > 0:
    result.setLen(length)
  else:
    raise newException(RsaKeyIncorrectError, "Incorrect private key")

proc getBytes*(sig: RsaSignature): seq[byte] =
  ## Serialize RSA signature ``sig`` to raw binary form and return it.
  doAssert(not isNil(sig))
  result = newSeq[byte](4096)
  let length = sig.toBytes(result)
  if length > 0:
    result.setLen(length)
  else:
    raise newException(RsaSignatureError, "Incorrect signature")

proc init*(key: var RsaPrivateKey, data: openarray[byte]): Asn1Status =
  ## Initialize RSA private key ``key`` from ASN.1 DER binary representation
  ## ``data``.
  ##
  ## Procedure returns ``Asn1Status``.
  var
    field, rawn, rawpube, rawprie, rawp, rawq, rawdp, rawdq, rawiq: Asn1Field
    version: uint64

  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 != 0'u64:
    return Asn1Status.Incorrect

  result = ib.read(rawn)
  if result != Asn1Status.Success:
    return
  if rawn.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawpube)
  if result != Asn1Status.Success:
    return
  if rawpube.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawprie)
  if result != Asn1Status.Success:
    return
  if rawprie.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawp)
  if result != Asn1Status.Success:
    return
  if rawp.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawq)
  if result != Asn1Status.Success:
    return
  if rawq.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawdp)
  if result != Asn1Status.Success:
    return
  if rawdp.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawdq)
  if result != Asn1Status.Success:
    return
  if rawdq.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = ib.read(rawiq)
  if result != Asn1Status.Success:
    return
  if rawiq.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  if len(rawn) >= (MinKeySize shr 3) and len(rawp) > 0 and len(rawq) > 0 and
     len(rawdp) > 0 and len(rawdq) > 0 and len(rawiq) > 0:
    key = new RsaPrivateKey
    key.buffer = @data
    key.pubk.n = cast[ptr cuchar](addr key.buffer[rawn.offset])
    key.pubk.e = cast[ptr cuchar](addr key.buffer[rawpube.offset])
    key.seck.p = cast[ptr cuchar](addr key.buffer[rawp.offset])
    key.seck.q = cast[ptr cuchar](addr key.buffer[rawq.offset])
    key.seck.dp = cast[ptr cuchar](addr key.buffer[rawdp.offset])
    key.seck.dq = cast[ptr cuchar](addr key.buffer[rawdq.offset])
    key.seck.iq = cast[ptr cuchar](addr key.buffer[rawiq.offset])
    key.pexp = cast[ptr cuchar](addr key.buffer[rawprie.offset])
    key.pubk.nlen = len(rawn)
    key.pubk.elen = len(rawpube)
    key.seck.plen = len(rawp)
    key.seck.qlen = len(rawq)
    key.seck.dplen = len(rawdp)
    key.seck.dqlen = len(rawdq)
    key.seck.iqlen = len(rawiq)
    key.pexplen = len(rawprie)
    key.seck.nBitlen = cast[uint32](len(rawn) shl 3)
    result = Asn1Status.Success
  else:
    result = Asn1Status.Incorrect

proc init*(key: var RsaPublicKey, data: openarray[byte]): Asn1Status =
  ## Initialize RSA public key ``key`` from ASN.1 DER binary representation
  ## ``data``.
  ##
  ## Procedure returns ``Asn1Status``.
  var field, rawn, rawe, oid: Asn1Field
  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(field)
  if result != Asn1Status.Success:
    return
  if field.kind != Asn1Tag.Oid:
    return Asn1Status.Incorrect
  if field != Asn1OidRsaEncryption:
    return Asn1Status.Incorrect

  result = ob.read(field)
  if result != Asn1Status.Success:
    return
  if field.kind != Asn1Tag.Null:
    return Asn1Status.Incorrect

  result = ib.read(field)
  if result != Asn1Status.Success:
    return
  if field.kind != Asn1Tag.BitString:
    return Asn1Status.Incorrect
  var vb = field.getBuffer()

  result = vb.read(field)
  if result != Asn1Status.Success:
    return
  if field.kind != Asn1Tag.Sequence:
    return Asn1Status.Incorrect
  var sb = field.getBuffer()

  result = sb.read(rawn)
  if result != Asn1Status.Success:
    return
  if rawn.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  result = sb.read(rawe)
  if result != Asn1Status.Success:
    return
  if rawn.kind != Asn1Tag.Integer:
    return Asn1Status.Incorrect

  if len(rawn) >= (MinKeySize shr 3) and len(rawe) > 0:
    key = new RsaPublicKey
    key.buffer = @data
    key.key.n = cast[ptr cuchar](addr key.buffer[rawn.offset])
    key.key.e = cast[ptr cuchar](addr key.buffer[rawe.offset])
    key.key.nlen = len(rawn)
    key.key.elen = len(rawe)
    result = Asn1Status.Success
  else:
    result = Asn1Status.Incorrect

proc init*(sig: var RsaSignature, data: openarray[byte]): Asn1Status =
  ## Initialize RSA signature ``sig`` from ASN.1 DER binary representation
  ## ``data``.
  ##
  ## Procedure returns ``Asn1Status``.
  result = Asn1Status.Incorrect
  if len(data) > 0:
    sig = new RsaSignature
    sig.buffer = @data
    result = Asn1Status.Success

proc init*[T: RsaPKI](sospk: var T, data: string): Asn1Status {.inline.} =
  ## Initialize EC `private key`, `public key` or `scalar` ``sospk`` from
  ## hexadecimal string representation ``data``.
  ##
  ## Procedure returns ``Asn1Status``.
  result = sospk.init(fromHex(data))

proc init*(t: typedesc[RsaPrivateKey], data: openarray[byte]): RsaPrivateKey =
  ## Initialize RSA private key from ASN.1 DER binary representation ``data``
  ## and return constructed object.
  let res = result.init(data)
  if res != Asn1Status.Success:
    raise newException(RsaKeyIncorrectError,
                       "Incorrect private key (" & $res & ")")

proc init*(t: typedesc[RsaPublicKey], data: openarray[byte]): RsaPublicKey =
  ## Initialize RSA public key from ASN.1 DER binary representation ``data``
  ## and return constructed object.
  let res = result.init(data)
  if res != Asn1Status.Success:
    raise newException(RsaKeyIncorrectError,
                       "Incorrect public key (" & $res & ")")

proc init*(t: typedesc[RsaSignature], data: openarray[byte]): RsaSignature =
  ## Initialize RSA signature from raw binary representation ``data`` and
  ## return constructed object.
  let res = result.init(data)
  if res != Asn1Status.Success:
    raise newException(RsaKeyIncorrectError,
                       "Incorrect signature (" & $res & ")")

proc init*[T: RsaPKI](t: typedesc[T], data: string): T {.inline.} =
  ## Initialize RSA `private key`, `public key` or `signature` from hexadecimal
  ## string representation ``data`` and return constructed object.
  result = t.init(fromHex(data))

proc `$`*(key: RsaPrivateKey): string =
  ## Return string representation of RSA private key.
  if isNil(key) or len(key.buffer) == 0:
    result = "Empty or uninitialized RSA key"
  else:
    result = "RSA key ("
    result.add($key.seck.nBitlen)
    result.add(" bits)\n")
    result.add("p   = ")
    result.add(toHex(getArray(key.buffer, key.seck.p, key.seck.plen)))
    result.add("\nq   = ")
    result.add(toHex(getArray(key.buffer, key.seck.q, key.seck.qlen)))
    result.add("\ndp  = ")
    result.add(toHex(getArray(key.buffer, key.seck.dp, key.seck.dplen)))
    result.add("\ndq  = ")
    result.add(toHex(getArray(key.buffer, key.seck.dq, key.seck.dqlen)))
    result.add("\niq  = ")
    result.add(toHex(getArray(key.buffer, key.seck.iq, key.seck.iqlen)))
    result.add("\npre = ")
    result.add(toHex(getArray(key.buffer, key.pexp, key.pexplen)))
    result.add("\nm   = ")
    result.add(toHex(getArray(key.buffer, key.pubk.n, key.pubk.nlen)))
    result.add("\npue = ")
    result.add(toHex(getArray(key.buffer, key.pubk.e, key.pubk.elen)))
    result.add("\n")

proc `$`*(key: RsaPublicKey): string =
  ## Return string representation of RSA public key.
  if isNil(key) or len(key.buffer) == 0:
    result = "Empty or uninitialized RSA key"
  else:
    let nbitlen = key.key.nlen shl 3
    result = "RSA key ("
    result.add($nbitlen)
    result.add(" bits)\nn = ")
    result.add(toHex(getArray(key.buffer, key.key.n, key.key.nlen)))
    result.add("\ne = ")
    result.add(toHex(getArray(key.buffer, key.key.e, key.key.elen)))
    result.add("\n")

proc `$`*(sig: RsaSignature): string =
  ## Return string representation of RSA signature.
  if isNil(sig) or len(sig.buffer) == 0:
    result = "Empty or uninitialized RSA signature"
  else:
    result = "RSA signature ("
    result.add(toHex(sig.buffer))
    result.add(")")

proc cmp(a: openarray[byte], b: openarray[byte]): bool =
  let alen = len(a)
  let blen = len(b)
  if alen == blen:
    if alen == 0:
      result = true
    else:
      var n = alen
      var res, diff: int
      while n > 0:
        dec(n)
        diff = int(a[n]) - int(b[n])
        res = (res and -not(diff)) or diff
      result = (res == 0)

proc `==`*(a, b: RsaPrivateKey): bool =
  ## Compare two RSA private keys for equality.
  ##
  ## Result is true if ``a`` and ``b`` are both ``nil`` or ``a`` and ``b`` are
  ## equal by value.
  if isNil(a) and isNil(b):
    result = true
  elif isNil(a) and (not isNil(b)):
    result = false
  elif isNil(b) and (not isNil(a)):
    result = false
  else:
    if a.seck.nBitlen == b.seck.nBitlen:
      if cast[int](a.seck.nBitlen) > 0:
        let r1 = cmp(getArray(a.buffer, a.seck.p, a.seck.plen),
                     getArray(b.buffer, b.seck.p, b.seck.plen))
        let r2 = cmp(getArray(a.buffer, a.seck.q, a.seck.qlen),
                     getArray(b.buffer, b.seck.q, b.seck.qlen))
        let r3 = cmp(getArray(a.buffer, a.seck.dp, a.seck.dplen),
                     getArray(b.buffer, b.seck.dp, b.seck.dplen))
        let r4 = cmp(getArray(a.buffer, a.seck.dq, a.seck.dqlen),
                     getArray(b.buffer, b.seck.dq, b.seck.dqlen))
        let r5 = cmp(getArray(a.buffer, a.seck.iq, a.seck.iqlen),
                     getArray(b.buffer, b.seck.iq, b.seck.iqlen))
        let r6 = cmp(getArray(a.buffer, a.pexp, a.pexplen),
                     getArray(b.buffer, b.pexp, b.pexplen))
        let r7 = cmp(getArray(a.buffer, a.pubk.n, a.pubk.nlen),
                     getArray(b.buffer, b.pubk.n, b.pubk.nlen))
        let r8 = cmp(getArray(a.buffer, a.pubk.e, a.pubk.elen),
                     getArray(b.buffer, b.pubk.e, b.pubk.elen))
        result = r1 and r2 and r3 and r4 and r5 and r6 and r7 and r8
      else:
        result = true

proc `==`*(a, b: RsaSignature): bool =
  ## Compare two RSA signatures for equality.
  if isNil(a) and isNil(b):
    result = true
  elif isNil(a) and (not isNil(b)):
    result = false
  elif isNil(b) and (not isNil(a)):
    result = false
  else:
    result = (a.buffer == b.buffer)

proc `==`*(a, b: RsaPublicKey): bool =
  ## Compare two RSA public keys for equality.
  if isNil(a) and isNil(b):
    result = true
  elif isNil(a) and (not isNil(b)):
    result = false
  elif isNil(b) and (not isNil(a)):
    result = false
  else:
    let r1 = cmp(getArray(a.buffer, a.key.n, a.key.nlen),
                 getArray(b.buffer, b.key.n, b.key.nlen))
    let r2 = cmp(getArray(a.buffer, a.key.e, a.key.elen),
                 getArray(b.buffer, b.key.e, b.key.elen))
    result = r1 and r2

proc sign*[T: byte|char](key: RsaPrivateKey,
                         message: openarray[T]): RsaSignature =
  ## Get RSA PKCS1.5 signature of data ``message`` using SHA256 and private
  ## key ``key``.
  doAssert(not isNil(key))
  var hc: BrHashCompatContext
  var hash: array[32, byte]
  var impl = BrRsaPkcs1SignGetDefault()
  result = new RsaSignature
  result.buffer = newSeq[byte]((key.seck.nBitlen + 7) shr 3)
  var kv = addr sha256Vtable
  kv.init(addr hc.vtable)
  if len(message) > 0:
    kv.update(addr hc.vtable, unsafeAddr message[0], len(message))
  else:
    kv.update(addr hc.vtable, nil, 0)
  kv.output(addr hc.vtable, addr hash[0])
  var oid = RsaOidSha256
  let res = impl(cast[ptr cuchar](addr oid[0]),
                 cast[ptr cuchar](addr hash[0]), len(hash),
                 addr key.seck, cast[ptr cuchar](addr result.buffer[0]))
  if res == 0:
    raise newException(RsaSignatureError, "Signature generation error")

proc verify*[T: byte|char](sig: RsaSignature, message: openarray[T],
                           pubkey: RsaPublicKey): bool {.inline.} =
  ## Verify RSA signature ``sig`` using public key ``pubkey`` and data
  ## ``message``.
  ##
  ## Return ``true`` if message verification succeeded, ``false`` if
  ## verification failed.
  doAssert((not isNil(sig)) and (not isNil(pubkey)))
  if len(sig.buffer) > 0:
    var hc: BrHashCompatContext
    var hash: array[32, byte]
    var check: array[32, byte]
    var impl = BrRsaPkcs1VrfyGetDefault()
    var kv = addr sha256Vtable
    kv.init(addr hc.vtable)
    if len(message) > 0:
      kv.update(addr hc.vtable, unsafeAddr message[0], len(message))
    else:
      kv.update(addr hc.vtable, nil, 0)
    kv.output(addr hc.vtable, addr hash[0])
    var oid = RsaOidSha256
    let res = impl(cast[ptr cuchar](addr sig.buffer[0]), len(sig.buffer),
                   cast[ptr cuchar](addr oid[0]),
                   len(check), addr pubkey.key, cast[ptr cuchar](addr check[0]))
    if res == 1:
      result = equalMem(addr check[0], addr hash[0], len(hash))