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Date: Wed, 21 Jan 2015 22:12:31 -0500
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From: David Vorick <david.vorick@gmail.com>
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Subject: Re: [Bitcoin-development] [softfork proposal] Strict DER signatures
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Seems like a good change to me.
On Wed, Jan 21, 2015 at 7:32 PM, Rusty Russell <rusty@rustcorp.com.au>
wrote:
> Pieter Wuille <pieter.wuille@gmail.com> writes:
> > Hello everyone,
> >
> > We've been aware of the risk of depending on OpenSSL for consensus
> > rules for a while, and were trying to get rid of this as part of BIP
> > 62 (malleability protection), which was however postponed due to
> > unforeseen complexities. The recent evens (see the thread titled
> > "OpenSSL 1.0.0p / 1.0.1k incompatible, causes blockchain rejection."
> > on this mailing list) have made it clear that the problem is very
> > real, however, and I would prefer to have a fundamental solution for
> > it sooner rather than later.
>
> OK, I worked up a clearer (but more verbose) version with fewer
> magic numbers. More importantly, feel free to steal the test cases.
>
> One weirdness is the restriction on maximum total length, rather than a
> 32 byte (33 with 0-prepad) limit on signatures themselves.
>
> Apologies for my babytalk C++. Am sure there's a neater way.
>
> /* Licensed under Creative Commons zero (public domain). */
> #include <vector>
> #include <cstdlib>
> #include <cassert>
>
> #ifdef CLARIFY
> bool ConsumeByte(const std::vector<unsigned char> &sig, size_t &off,
> unsigned int &val)
> {
> if (off >= sig.size()) return false;
>
> val = sig[off++];
> return true;
> }
>
> bool ConsumeTypeByte(const std::vector<unsigned char> &sig, size_t &off,
> unsigned int t)
> {
> unsigned int type;
> if (!ConsumeByte(sig, off, type)) return false;
>
> return (type == t);
> }
>
> bool ConsumeNonZeroLength(const std::vector<unsigned char> &sig, size_t
> &off,
> unsigned int &len)
> {
> if (!ConsumeByte(sig, off, len)) return false;
>
> // Zero-length integers are not allowed.
> return (len != 0);
> }
>
> bool ConsumeNumber(const std::vector<unsigned char> &sig, size_t &off,
> unsigned int len)
> {
> // Length of number should be within signature.
> if (off + len > sig.size()) return false;
>
> // Negative numbers are not allowed.
> if (sig[off] & 0x80) return false;
>
> // Zero bytes at the start are not allowed, unless it would
> // otherwise be interpreted as a negative number.
> if (len > 1 && (sig[off] == 0x00) && !(sig[off+1] & 0x80)) return
> false;
>
> // Consume number itself.
> off += len;
> return true;
> }
>
> // Consume a DER encoded integer, update off if successful.
> bool ConsumeDERInteger(const std::vector<unsigned char> &sig, size_t &off)
> {
> unsigned int len;
>
> // Type byte must be "integer"
> if (!ConsumeTypeByte(sig, off, 0x02)) return false;
> if (!ConsumeNonZeroLength(sig, off, len)) return false;
> // Now the BE encoded value itself.
> if (!ConsumeNumber(sig, off, len)) return false;
>
> return true;
> }
>
> bool IsValidSignatureEncoding(const std::vector<unsigned char> &sig) {
> // Format: 0x30 [total-length] 0x02 [R-length] [R] 0x02 [S-length] [S]
> [sighash]
> // * total-length: 1-byte length descriptor of everything that follows,
> // excluding the sighash byte.
> // * R-length: 1-byte length descriptor of the R value that follows.
> // * R: arbitrary-length big-endian encoded R value. It cannot start
> with any
> // null bytes, unless the first byte that follows is 0x80 or
> higher, in which
> // case a single null byte is required.
> // * S-length: 1-byte length descriptor of the S value that follows.
> // * S: arbitrary-length big-endian encoded S value. The same rules
> apply.
> // * sighash: 1-byte value indicating what data is hashed.
>
> // Accept empty signature as correctly encoded (but invalid) signature,
> // even though it is not strictly DER.
> if (sig.size() == 0) return true;
>
> // Maximum size constraint.
> if (sig.size() > 73) return false;
>
> size_t off = 0;
>
> // A signature is of type "compound".
> if (!ConsumeTypeByte(sig, off, 0x30)) return false;
>
> unsigned int len;
> if (!ConsumeNonZeroLength(sig, off, len)) return false;
>
> // Make sure the length covers the rest (except sighash).
> if (len + 1 != sig.size() - off) return false;
>
> // Check R value.
> if (!ConsumeDERInteger(sig, off)) return false;
>
> // Check S value.
> if (!ConsumeDERInteger(sig, off)) return false;
>
> // There should exactly one byte left (the sighash).
> return off + 1 == sig.size() ? true : false;
> }
> #else
> bool IsValidSignatureEncoding(const std::vector<unsigned char> &sig) {
> // Format: 0x30 [total-length] 0x02 [R-length] [R] 0x02 [S-length] [S]
> [sighash]
> // * total-length: 1-byte length descriptor of everything that follows,
> // excluding the sighash byte.
> // * R-length: 1-byte length descriptor of the R value that follows.
> // * R: arbitrary-length big-endian encoded R value. It must use the
> shortest
> // possible encoding for a positive integers (which means no null
> bytes at
> // the start, except a single one when the next byte has its
> highest bit set).
> // * S-length: 1-byte length descriptor of the S value that follows.
> // * S: arbitrary-length big-endian encoded S value. The same rules
> apply.
> // * sighash: 1-byte value indicating what data is hashed (not part of
> the DER
> // signature)
>
> // Accept empty signature as correctly encoded (but invalid) signature,
> // even though it is not strictly DER. This avoids needing full DER
> signatures
> // in places where any invalid signature would do. Given that the
> empty string is
> // always invalid as signature, this is safe.
> if (sig.size() == 0) return true;
>
> // Minimum and maximum size constraints.
> if (sig.size() < 9) return false;
> if (sig.size() > 73) return false;
>
> // A signature is of type 0x30 (compound).
> if (sig[0] != 0x30) return false;
>
> // Make sure the length covers the entire signature.
> if (sig[1] != sig.size() - 3) return false;
>
> // Extract the length of the R element.
> unsigned int lenR = sig[3];
>
> // Make sure the length of the S element is still inside the signature.
> if (5 + lenR >= sig.size()) return false;
>
> // Extract the length of the S element.
> unsigned int lenS = sig[5 + lenR];
>
> // Verify that the length of the signature matches the sum of the
> length
> // of the elements.
> if ((size_t)(lenR + lenS + 7) != sig.size()) return false;
>
> // Check whether the R element is an integer.
> if (sig[2] != 0x02) return false;
>
> // Zero-length integers are not allowed for R.
> if (lenR == 0) return false;
>
> // Negative numbers are not allowed for R.
> if (sig[4] & 0x80) return false;
>
> // Null bytes at the start of R are not allowed, unless R would
> // otherwise be interpreted as a negative number.
> if (lenR > 1 && (sig[4] == 0x00) && !(sig[5] & 0x80)) return false;
>
> // Check whether the S element is an integer.
> if (sig[lenR + 4] != 0x02) return false;
>
> // Zero-length integers are not allowed for S.
> if (lenS == 0) return false;
>
> // Negative numbers are not allowed for S.
> if (sig[lenR + 6] & 0x80) return false;
>
> // Null bytes at the start of S are not allowed, unless S would
> otherwise be
> // interpreted as a negative number.
> if (lenS > 1 && (sig[lenR + 6] == 0x00) && !(sig[lenR + 7] & 0x80))
> return false;
>
> return true;
> }
> #endif
>
> #define COMPOUND 0x30
> #define NOT_COMPOUND 0x31
>
> // Len gets adjusted by check() to be actual length with this offset.
> #define LEN_OK 0
> #define LEN_TOO_BIG 1
> #define LEN_TOO_SMALL 0xff
>
> #define INT 0x02
> #define NOT_INT 0x03
>
> #define MINIMAL_SIGLEN 1
> #define MINIMAL_SIGVAL 0x0
>
> #define NORMAL_SIGLEN 32
> #define NORMAL_SIGVAL(S) S, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, \
> 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, \
> 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17, \
> 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f
>
> // 33 bytes is possible, with 0 prepended.
> #define MAXIMAL_SIGLEN 33
> #define MAXIMAL_SIGVAL(S) NORMAL_SIGVAL(S), 0x20
>
> #define OVERSIZE_SIGLEN 34
> #define OVERSIZE_SIGVAL(S) MAXIMAL_SIGVAL(S), 0x21
>
> #define ZEROPAD_SIGLEN (1 + NORMAL_SIGLEN)
> #define ZEROPAD_SIGVAL(S) 00, NORMAL_SIGVAL(S)
>
> #define SIGHASH 0xf0
>
> static bool check(const std::vector<unsigned char> &sig)
> {
> std::vector<unsigned char> fixed = sig;
>
> // Fixup length
> if (fixed.size() > 1)
> fixed[1] += fixed.size() - 3;
> return IsValidSignatureEncoding(fixed);
> }
>
> #define good(arr) assert(check(std::vector<unsigned char>(arr,
> arr+sizeof(arr))))
> #define bad(arr) assert(!check(std::vector<unsigned char>(arr,
> arr+sizeof(arr))))
>
> // The OK cases.
> static unsigned char zerolen[] = { };
> static unsigned char normal[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char min_r[] = { COMPOUND, LEN_OK,
> INT, MINIMAL_SIGLEN, MINIMAL_SIGVAL,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char min_s[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),
> INT, MINIMAL_SIGLEN, MINIMAL_SIGVAL,
> SIGHASH };
> static unsigned char max_r[] = { COMPOUND, LEN_OK,
> INT, MAXIMAL_SIGLEN, MAXIMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char max_s[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),
> INT, MAXIMAL_SIGLEN, MAXIMAL_SIGVAL(0x2),
> SIGHASH };
> // As long as total size doesn't go over, a single sig is allowed > 33
> bytes
> static unsigned char wierd_s_len[] = { COMPOUND, LEN_OK,
> INT, OVERSIZE_SIGLEN,
> OVERSIZE_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char wierd_r_len[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, OVERSIZE_SIGLEN,
> OVERSIZE_SIGVAL(0x2),
> SIGHASH };
> static unsigned char zeropad_s[] = { COMPOUND, LEN_OK,
> INT, ZEROPAD_SIGLEN,
> ZEROPAD_SIGVAL(0x81),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char zeropad_r[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, ZEROPAD_SIGLEN,
> ZEROPAD_SIGVAL(0x82),
> SIGHASH };
>
>
> // The fail cases.
> static unsigned char not_compound[] = { NOT_COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char short_len[] = { COMPOUND, LEN_TOO_SMALL,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char long_len[] = { COMPOUND, LEN_TOO_BIG,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char r_notint[] = { COMPOUND, LEN_OK,
> NOT_INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char s_notint[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),
> NOT_INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char s_oversig[] = { COMPOUND, LEN_OK,
> INT, OVERSIZE_SIGLEN,
> OVERSIZE_SIGVAL(0x1),
> INT, MAXIMAL_SIGLEN,
> MAXIMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char r_oversig[] = { COMPOUND, LEN_OK,
> INT, MAXIMAL_SIGLEN,
> MAXIMAL_SIGVAL(0x1),
> INT, OVERSIZE_SIGLEN,
> OVERSIZE_SIGVAL(0x2),
> SIGHASH };
> static unsigned char s_negative[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x81),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char r_negative[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x82),
> SIGHASH };
> static unsigned char zeropad_bad_s[] = { COMPOUND, LEN_OK,
> INT, ZEROPAD_SIGLEN,
> ZEROPAD_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char zeropad_bad_r[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, ZEROPAD_SIGLEN,
> ZEROPAD_SIGVAL(0x2),
> SIGHASH };
> static unsigned char missing_sighash[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2) };
> static unsigned char extra_byte[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH, 0 };
>
> // Bad signature lengths
> static unsigned char zerolen_r[] = { COMPOUND, LEN_OK,
> INT, 0,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char zerolen_s[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, 0,
> SIGHASH };
> static unsigned char overlen_r_by_1[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN + 1 + 1 +
> NORMAL_SIGLEN + 1 + 1, NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char overlen_s_by_1[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN+1+1,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char underlen_r_by_1[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN-1,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
> static unsigned char underlen_s_by_1[] = { COMPOUND, LEN_OK,
> INT, NORMAL_SIGLEN,
> NORMAL_SIGVAL(0x1),
> INT, NORMAL_SIGLEN-1,
> NORMAL_SIGVAL(0x2),
> SIGHASH };
>
> int main()
> {
> good(zerolen);
> good(normal);
> good(min_r);
> good(min_s);
> good(max_r);
> good(max_s);
> good(wierd_s_len);
> good(wierd_r_len);
> good(zeropad_s);
> good(zeropad_r);
>
> // Try different amounts of truncation.
> for (size_t i = 1; i < sizeof(normal)-1; i++)
> assert(!check(std::vector<unsigned char>(normal, normal+i)));
>
> bad(not_compound);
> bad(short_len);
> bad(long_len);
> bad(r_notint);
> bad(s_notint);
> bad(s_oversig);
> bad(r_oversig);
> bad(s_negative);
> bad(r_negative);
> bad(s_negative);
> bad(r_negative);
> bad(zeropad_bad_s);
> bad(zeropad_bad_r);
> bad(zerolen_r);
> bad(zerolen_s);
> bad(overlen_r_by_1);
> bad(overlen_s_by_1);
> bad(underlen_r_by_1);
> bad(underlen_s_by_1);
> bad(missing_sighash);
> bad(extra_byte);
>
> return 0;
> }
>
>
>
>
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--f46d04430682eb53f0050d350a13
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
<div dir=3D"ltr">Seems like a good change to me.<br></div><div class=3D"gma=
il_extra"><br><div class=3D"gmail_quote">On Wed, Jan 21, 2015 at 7:32 PM, R=
usty Russell <span dir=3D"ltr"><<a href=3D"mailto:rusty@rustcorp.com.au"=
target=3D"_blank">rusty@rustcorp.com.au</a>></span> wrote:<br><blockquo=
te class=3D"gmail_quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc so=
lid;padding-left:1ex"><span class=3D"">Pieter Wuille <<a href=3D"mailto:=
pieter.wuille@gmail.com">pieter.wuille@gmail.com</a>> writes:<br>
> Hello everyone,<br>
><br>
> We've been aware of the risk of depending on OpenSSL for consensus=
<br>
> rules for a while, and were trying to get rid of this as part of BIP<b=
r>
> 62 (malleability protection), which was however postponed due to<br>
> unforeseen complexities. The recent evens (see the thread titled<br>
> "OpenSSL 1.0.0p / 1.0.1k incompatible, causes blockchain rejectio=
n."<br>
> on this mailing list) have made it clear that the problem is very<br>
> real, however, and I would prefer to have a fundamental solution for<b=
r>
> it sooner rather than later.<br>
<br>
</span>OK, I worked up a clearer (but more verbose) version with fewer<br>
magic numbers.=C2=A0 More importantly, feel free to steal the test cases.<b=
r>
<br>
One weirdness is the restriction on maximum total length, rather than a<br>
32 byte (33 with 0-prepad) limit on signatures themselves.<br>
<br>
Apologies for my babytalk C++.=C2=A0 Am sure there's a neater way.<br>
<br>
/* Licensed under Creative Commons zero (public domain). */<br>
#include <vector><br>
#include <cstdlib><br>
#include <cassert><br>
<br>
#ifdef CLARIFY<br>
bool ConsumeByte(const std::vector<unsigned char> &sig, size_t &a=
mp;off,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0unsigned int =
&val)<br>
{<br>
=C2=A0 =C2=A0 if (off >=3D sig.size()) return false;<br>
<br>
=C2=A0 =C2=A0 val =3D sig[off++];<br>
=C2=A0 =C2=A0 return true;<br>
}<br>
<br>
bool ConsumeTypeByte(const std::vector<unsigned char> &sig, size_=
t &off,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0unsigned int t)<br>
{<br>
=C2=A0 =C2=A0 unsigned int type;<br>
=C2=A0 =C2=A0 if (!ConsumeByte(sig, off, type)) return false;<br>
<br>
=C2=A0 =C2=A0 return (type =3D=3D t);<br>
}<br>
<br>
bool ConsumeNonZeroLength(const std::vector<unsigned char> &sig, =
size_t &off,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 unsigned int &len)<br>
{<br>
=C2=A0 =C2=A0 if (!ConsumeByte(sig, off, len)) return false;<br>
<br>
=C2=A0 =C2=A0 // Zero-length integers are not allowed.<br>
=C2=A0 =C2=A0 return (len !=3D 0);<br>
}<br>
<br>
bool ConsumeNumber(const std::vector<unsigned char> &sig, size_t =
&off,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0unsign=
ed int len)<br>
{<br>
=C2=A0 =C2=A0 // Length of number should be within signature.<br>
=C2=A0 =C2=A0 if (off + len > sig.size()) return false;<br>
<br>
=C2=A0 =C2=A0 // Negative numbers are not allowed.<br>
=C2=A0 =C2=A0 if (sig[off] & 0x80) return false;<br>
<br>
=C2=A0 =C2=A0 // Zero bytes at the start are not allowed, unless it would<b=
r>
=C2=A0 =C2=A0 // otherwise be interpreted as a negative number.<br>
=C2=A0 =C2=A0 if (len > 1 && (sig[off] =3D=3D 0x00) && !=
(sig[off+1] & 0x80)) return false;<br>
<br>
=C2=A0 =C2=A0 // Consume number itself.<br>
=C2=A0 =C2=A0 off +=3D len;<br>
=C2=A0 =C2=A0 return true;<br>
}<br>
<br>
// Consume a DER encoded integer, update off if successful.<br>
bool ConsumeDERInteger(const std::vector<unsigned char> &sig, siz=
e_t &off) {<br>
=C2=A0 =C2=A0 unsigned int len;<br>
<br>
=C2=A0 =C2=A0 // Type byte must be "integer"<br>
=C2=A0 =C2=A0 if (!ConsumeTypeByte(sig, off, 0x02)) return false;<br>
=C2=A0 =C2=A0 if (!ConsumeNonZeroLength(sig, off, len)) return false;<br>
=C2=A0 =C2=A0 // Now the BE encoded value itself.<br>
=C2=A0 =C2=A0 if (!ConsumeNumber(sig, off, len)) return false;<br>
<br>
=C2=A0 =C2=A0 return true;<br>
}<br>
<br>
bool IsValidSignatureEncoding(const std::vector<unsigned char> &s=
ig) {<br>
=C2=A0 =C2=A0 // Format: 0x30 [total-length] 0x02 [R-length] [R] 0x02 [S-le=
ngth] [S] [sighash]<br>
=C2=A0 =C2=A0 // * total-length: 1-byte length descriptor of everything tha=
t follows,<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0excluding the sighash byte.<br>
=C2=A0 =C2=A0 // * R-length: 1-byte length descriptor of the R value that f=
ollows.<br>
=C2=A0 =C2=A0 // * R: arbitrary-length big-endian encoded R value. It canno=
t start with any<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0null bytes, unless the first byte that =
follows is 0x80 or higher, in which<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0case a single null byte is required.<br=
>
=C2=A0 =C2=A0 // * S-length: 1-byte length descriptor of the S value that f=
ollows.<br>
=C2=A0 =C2=A0 // * S: arbitrary-length big-endian encoded S value. The same=
rules apply.<br>
=C2=A0 =C2=A0 // * sighash: 1-byte value indicating what data is hashed.<br=
>
<br>
=C2=A0 =C2=A0 // Accept empty signature as correctly encoded (but invalid) =
signature,<br>
=C2=A0 =C2=A0 // even though it is not strictly DER.<br>
=C2=A0 =C2=A0 if (sig.size() =3D=3D 0) return true;<br>
<br>
=C2=A0 =C2=A0 // Maximum size constraint.<br>
=C2=A0 =C2=A0 if (sig.size() > 73) return false;<br>
<br>
=C2=A0 =C2=A0 size_t off =3D 0;<br>
<br>
=C2=A0 =C2=A0 // A signature is of type "compound".<br>
=C2=A0 =C2=A0 if (!ConsumeTypeByte(sig, off, 0x30)) return false;<br>
<br>
=C2=A0 =C2=A0 unsigned int len;<br>
=C2=A0 =C2=A0 if (!ConsumeNonZeroLength(sig, off, len)) return false;<br>
<br>
=C2=A0 =C2=A0 // Make sure the length covers the rest (except sighash).<br>
=C2=A0 =C2=A0 if (len + 1 !=3D sig.size() - off) return false;<br>
<br>
=C2=A0 =C2=A0 // Check R value.<br>
=C2=A0 =C2=A0 if (!ConsumeDERInteger(sig, off)) return false;<br>
<br>
=C2=A0 =C2=A0 // Check S value.<br>
=C2=A0 =C2=A0 if (!ConsumeDERInteger(sig, off)) return false;<br>
<br>
=C2=A0 =C2=A0 // There should exactly one byte left (the sighash).<br>
=C2=A0 =C2=A0 return off + 1 =3D=3D sig.size() ? true : false;<br>
}<br>
#else<br>
bool IsValidSignatureEncoding(const std::vector<unsigned char> &s=
ig) {<br>
=C2=A0 =C2=A0 // Format: 0x30 [total-length] 0x02 [R-length] [R] 0x02 [S-le=
ngth] [S] [sighash]<br>
=C2=A0 =C2=A0 // * total-length: 1-byte length descriptor of everything tha=
t follows,<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0excluding the sighash byte.<br>
=C2=A0 =C2=A0 // * R-length: 1-byte length descriptor of the R value that f=
ollows.<br>
=C2=A0 =C2=A0 // * R: arbitrary-length big-endian encoded R value. It must =
use the shortest<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0possible encoding for a positive intege=
rs (which means no null bytes at<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0the start, except a single one when the=
next byte has its highest bit set).<br>
=C2=A0 =C2=A0 // * S-length: 1-byte length descriptor of the S value that f=
ollows.<br>
=C2=A0 =C2=A0 // * S: arbitrary-length big-endian encoded S value. The same=
rules apply.<br>
=C2=A0 =C2=A0 // * sighash: 1-byte value indicating what data is hashed (no=
t part of the DER<br>
=C2=A0 =C2=A0 //=C2=A0 =C2=A0 =C2=A0signature)<br>
<br>
=C2=A0 =C2=A0 // Accept empty signature as correctly encoded (but invalid) =
signature,<br>
=C2=A0 =C2=A0 // even though it is not strictly DER. This avoids needing fu=
ll DER signatures<br>
=C2=A0 =C2=A0 // in places where any invalid signature would do. Given that=
the empty string is<br>
=C2=A0 =C2=A0 // always invalid as signature, this is safe.<br>
=C2=A0 =C2=A0 if (sig.size() =3D=3D 0) return true;<br>
<br>
=C2=A0 =C2=A0 // Minimum and maximum size constraints.<br>
=C2=A0 =C2=A0 if (sig.size() < 9) return false;<br>
=C2=A0 =C2=A0 if (sig.size() > 73) return false;<br>
<br>
=C2=A0 =C2=A0 // A signature is of type 0x30 (compound).<br>
=C2=A0 =C2=A0 if (sig[0] !=3D 0x30) return false;<br>
<br>
=C2=A0 =C2=A0 // Make sure the length covers the entire signature.<br>
=C2=A0 =C2=A0 if (sig[1] !=3D sig.size() - 3) return false;<br>
<br>
=C2=A0 =C2=A0 // Extract the length of the R element.<br>
=C2=A0 =C2=A0 unsigned int lenR =3D sig[3];<br>
<br>
=C2=A0 =C2=A0 // Make sure the length of the S element is still inside the =
signature.<br>
=C2=A0 =C2=A0 if (5 + lenR >=3D sig.size()) return false;<br>
<br>
=C2=A0 =C2=A0 // Extract the length of the S element.<br>
=C2=A0 =C2=A0 unsigned int lenS =3D sig[5 + lenR];<br>
<br>
=C2=A0 =C2=A0 // Verify that the length of the signature matches the sum of=
the length<br>
=C2=A0 =C2=A0 // of the elements.<br>
=C2=A0 =C2=A0 if ((size_t)(lenR + lenS + 7) !=3D sig.size()) return false;<=
br>
<br>
=C2=A0 =C2=A0 // Check whether the R element is an integer.<br>
=C2=A0 =C2=A0 if (sig[2] !=3D 0x02) return false;<br>
<br>
=C2=A0 =C2=A0 // Zero-length integers are not allowed for R.<br>
=C2=A0 =C2=A0 if (lenR =3D=3D 0) return false;<br>
<br>
=C2=A0 =C2=A0 // Negative numbers are not allowed for R.<br>
=C2=A0 =C2=A0 if (sig[4] & 0x80) return false;<br>
<br>
=C2=A0 =C2=A0 // Null bytes at the start of R are not allowed, unless R wou=
ld<br>
=C2=A0 =C2=A0 // otherwise be interpreted as a negative number.<br>
=C2=A0 =C2=A0 if (lenR > 1 && (sig[4] =3D=3D 0x00) && !(=
sig[5] & 0x80)) return false;<br>
<br>
=C2=A0 =C2=A0 // Check whether the S element is an integer.<br>
=C2=A0 =C2=A0 if (sig[lenR + 4] !=3D 0x02) return false;<br>
<br>
=C2=A0 =C2=A0 // Zero-length integers are not allowed for S.<br>
=C2=A0 =C2=A0 if (lenS =3D=3D 0) return false;<br>
<br>
=C2=A0 =C2=A0 // Negative numbers are not allowed for S.<br>
=C2=A0 =C2=A0 if (sig[lenR + 6] & 0x80) return false;<br>
<br>
=C2=A0 =C2=A0 // Null bytes at the start of S are not allowed, unless S wou=
ld otherwise be<br>
<span class=3D"">=C2=A0 =C2=A0 // interpreted as a negative number.<br>
=C2=A0 =C2=A0 if (lenS > 1 && (sig[lenR + 6] =3D=3D 0x00) &&=
amp; !(sig[lenR + 7] & 0x80)) return false;<br>
<br>
</span>=C2=A0 =C2=A0 return true;<br>
}<br>
#endif<br>
<br>
#define COMPOUND 0x30<br>
#define NOT_COMPOUND 0x31<br>
<br>
// Len gets adjusted by check() to be actual length with this offset.<br>
#define LEN_OK 0<br>
#define LEN_TOO_BIG 1<br>
#define LEN_TOO_SMALL 0xff<br>
<br>
#define INT 0x02<br>
#define NOT_INT 0x03<br>
<br>
#define MINIMAL_SIGLEN 1<br>
#define MINIMAL_SIGVAL 0x0<br>
<br>
#define NORMAL_SIGLEN 32<br>
#define NORMAL_SIGVAL(S) S, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, \<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 \<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 \<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f<=
br>
<br>
// 33 bytes is possible, with 0 prepended.<br>
#define MAXIMAL_SIGLEN 33<br>
#define MAXIMAL_SIGVAL(S) NORMAL_SIGVAL(S), 0x20<br>
<br>
#define OVERSIZE_SIGLEN 34<br>
#define OVERSIZE_SIGVAL(S) MAXIMAL_SIGVAL(S), 0x21<br>
<br>
#define ZEROPAD_SIGLEN (1 + NORMAL_SIGLEN)<br>
#define ZEROPAD_SIGVAL(S) 00, NORMAL_SIGVAL(S)<br>
<br>
#define SIGHASH 0xf0<br>
<br>
static bool check(const std::vector<unsigned char> &sig)<br>
{<br>
=C2=A0 =C2=A0 std::vector<unsigned char> fixed =3D sig;<br>
<br>
=C2=A0 =C2=A0 // Fixup length<br>
=C2=A0 =C2=A0 if (fixed.size() > 1)<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 fixed[1] +=3D fixed.size() - 3;<br>
=C2=A0 =C2=A0 return IsValidSignatureEncoding(fixed);<br>
}<br>
<br>
#define good(arr) assert(check(std::vector<unsigned char>(arr, arr+si=
zeof(arr))))<br>
#define bad(arr) assert(!check(std::vector<unsigned char>(arr, arr+si=
zeof(arr))))<br>
<br>
// The OK cases.<br>
static unsigned char zerolen[] =3D { };<br>
static unsigned char normal[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NORMAL_SI=
GVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NORMAL_SI=
GVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char min_r[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MINIMAL_SIGLEN, MINIMAL_S=
IGVAL,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGLEN, NORMAL_SIG=
VAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char min_s[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGLEN, NORMAL_SIG=
VAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MINIMAL_SIGLEN, MINIMAL_S=
IGVAL,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char max_r[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MAXIMAL_SIGLEN, MAXIMAL_S=
IGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGLEN, NORMAL_SIG=
VAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char max_s[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGLEN, NORMAL_SIG=
VAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MAXIMAL_SIGLEN, MAXIMAL_S=
IGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
// As long as total size doesn't go over, a single sig is allowed > =
33 bytes<br>
static unsigned char wierd_s_len[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, OVER=
SIZE_SIGLEN, OVERSIZE_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORM=
AL_SIGLEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH }=
;<br>
static unsigned char wierd_r_len[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORM=
AL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, OVER=
SIZE_SIGLEN, OVERSIZE_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH }=
;<br>
static unsigned char zeropad_s[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, ZEROPAD_SIG=
LEN, ZEROPAD_SIGVAL(0x81),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char zeropad_r[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, ZEROPAD_SIG=
LEN, ZEROPAD_SIGVAL(0x82),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
<br>
<br>
// The fail cases.<br>
static unsigned char not_compound[] =3D { NOT_COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NOR=
MAL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NOR=
MAL_SIGLEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH =
};<br>
static unsigned char short_len[] =3D { COMPOUND, LEN_TOO_SMALL,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char long_len[] =3D { COMPOUND, LEN_TOO_BIG,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NO=
RMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NO=
RMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char r_notint[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 NOT_INT, NORMAL_SIGLEN=
, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NO=
RMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char s_notint[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIGLEN, NO=
RMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 NOT_INT, NORMAL_SIGLEN=
, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char s_oversig[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, OVERSIZE_SI=
GLEN, OVERSIZE_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MAXIMAL_SIG=
LEN, MAXIMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char r_oversig[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, MAXIMAL_SIG=
LEN, MAXIMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, OVERSIZE_SI=
GLEN, OVERSIZE_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char s_negative[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x81),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char r_negative[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x82),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH };<br>
static unsigned char zeropad_bad_s[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0IN=
T, ZEROPAD_SIGLEN, ZEROPAD_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0IN=
T, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SI=
GHASH };<br>
static unsigned char zeropad_bad_r[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0IN=
T, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0IN=
T, ZEROPAD_SIGLEN, ZEROPAD_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SI=
GHASH };<br>
static unsigned char missing_sighash[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2) };<br>
static unsigned char extra_byte[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 INT, NORMAL_SIG=
LEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 SIGHASH, 0 };<b=
r>
<br>
// Bad signature lengths<br>
static unsigned char zerolen_r[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, 0,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char zerolen_s[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, NORMAL_SIGL=
EN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0INT, 0,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0SIGHASH };<br>
static unsigned char overlen_r_by_1[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 I=
NT, NORMAL_SIGLEN + 1 + 1 + NORMAL_SIGLEN + 1 + 1, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 I=
NT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 S=
IGHASH };<br>
static unsigned char overlen_s_by_1[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 I=
NT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 I=
NT, NORMAL_SIGLEN+1+1, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 S=
IGHASH };<br>
static unsigned char underlen_r_by_1[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN-1, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0SIGHASH };<br>
static unsigned char underlen_s_by_1[] =3D { COMPOUND, LEN_OK,<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN, NORMAL_SIGVAL(0x1),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0INT, NORMAL_SIGLEN-1, NORMAL_SIGVAL(0x2),<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0SIGHASH };<br>
<br>
int main()<br>
{<br>
=C2=A0 =C2=A0 good(zerolen);<br>
=C2=A0 =C2=A0 good(normal);<br>
=C2=A0 =C2=A0 good(min_r);<br>
=C2=A0 =C2=A0 good(min_s);<br>
=C2=A0 =C2=A0 good(max_r);<br>
=C2=A0 =C2=A0 good(max_s);<br>
=C2=A0 =C2=A0 good(wierd_s_len);<br>
=C2=A0 =C2=A0 good(wierd_r_len);<br>
=C2=A0 =C2=A0 good(zeropad_s);<br>
=C2=A0 =C2=A0 good(zeropad_r);<br>
<br>
=C2=A0 =C2=A0 // Try different amounts of truncation.<br>
=C2=A0 =C2=A0 for (size_t i =3D 1; i < sizeof(normal)-1; i++)<br>
=C2=A0 =C2=A0 =C2=A0 =C2=A0 assert(!check(std::vector<unsigned char>(=
normal, normal+i)));<br>
<br>
=C2=A0 =C2=A0 bad(not_compound);<br>
=C2=A0 =C2=A0 bad(short_len);<br>
=C2=A0 =C2=A0 bad(long_len);<br>
=C2=A0 =C2=A0 bad(r_notint);<br>
=C2=A0 =C2=A0 bad(s_notint);<br>
=C2=A0 =C2=A0 bad(s_oversig);<br>
=C2=A0 =C2=A0 bad(r_oversig);<br>
=C2=A0 =C2=A0 bad(s_negative);<br>
=C2=A0 =C2=A0 bad(r_negative);<br>
=C2=A0 =C2=A0 bad(s_negative);<br>
=C2=A0 =C2=A0 bad(r_negative);<br>
=C2=A0 =C2=A0 bad(zeropad_bad_s);<br>
=C2=A0 =C2=A0 bad(zeropad_bad_r);<br>
=C2=A0 =C2=A0 bad(zerolen_r);<br>
=C2=A0 =C2=A0 bad(zerolen_s);<br>
=C2=A0 =C2=A0 bad(overlen_r_by_1);<br>
=C2=A0 =C2=A0 bad(overlen_s_by_1);<br>
=C2=A0 =C2=A0 bad(underlen_r_by_1);<br>
=C2=A0 =C2=A0 bad(underlen_s_by_1);<br>
=C2=A0 =C2=A0 bad(missing_sighash);<br>
=C2=A0 =C2=A0 bad(extra_byte);<br>
<br>
=C2=A0 =C2=A0 return 0;<br>
<div class=3D"HOEnZb"><div class=3D"h5">}<br>
<br>
<br>
<br>
---------------------------------------------------------------------------=
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</div></div></blockquote></div><br></div>
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