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ECDSA r, s encoding as a signature

this link doesnt seem to add up, any suggestions?

closed as unclear what you're asking by Andrew Chow, Pieter Wuille, MCCCS, cdecker, Murch Sep 5 '17 at 20:47

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  • Could you clarify what "doesn't seem to add up" and what you want suggestions for? Your question is very unclear. – Andrew Chow Aug 29 '17 at 13:49
  • yeah, trying to make this work for 8 or more hours, feeling a bit off im trying to figure out how to edit out the parts from the signature so i could get the raw R's and S's what confises me is the part when the length is an uneven number of bytes, lets say 33, is there a way to circumvent this? is there a bitcoin suit that is "gettable" from the net that does all of that for you? – user3700810 Aug 29 '17 at 14:10
  • What about the length being odd confuses you? It is just an array of bytes which you then interpret as an integer. – Andrew Chow Aug 29 '17 at 15:16
4

The structure of a DER encoded ECDSA signature is as follows:

enter image description here

30 identifies a SEQUENCE in ASN1 encoding, which is followed by the length of z (the sequence). r and scan be either 32 or 33 bytes long, depending on how big the DER encoded values are. r and s are always leaded by 02, which identify an integer value in ASN1. Finally, the tailing (ht) byte represents the hashtype

In order to parse a signature to extract both values you should check their length, which is always 1 byte long, and extract the value depending on the result. Here's the code to do so:

def parse_element(hex_str, offset, element_size):
    """
    :param hex_str: string to parse the element from.
    :type hex_str: hex str
    :param offset: initial position of the object inside the hex_str.
    :type offset: int
    :param element_size: size of the element to extract.
    :type element_size: int
    :return: The extracted element from the provided string, and the updated offset after extracting it.
    :rtype tuple(str, int)
    """

    return hex_str[offset:offset+element_size], offset+element_size


def dissect_signature(hex_sig):
    """
    Extracts the r, s and ht components from a Bitcoin ECDSA signature.
    :param hex_sig: Signature in  hex format.
    :type hex_sig: hex str
    :return: r, s, t as a tuple.
    :rtype: tuple(str, str, str)
    """

    offset = 0
    # Check the sig contains at least the size and sequence marker
    assert len(hex_sig) > 4, "Wrong signature format."
    sequence, offset = parse_element(hex_sig, offset, 2)
    # Check sequence marker is correct
    assert sequence == '30', "Wrong sequence marker."
    signature_length, offset = parse_element(hex_sig, offset, 2)
    # Check the length of the remaining part matches the length of the signature + the length of the hashflag (1 byte)
    assert len(hex_sig[offset:])/2 == int(signature_length, 16) + 1, "Wrong length."
    # Get r
    marker, offset = parse_element(hex_sig, offset, 2)
    assert marker == '02', "Wrong r marker."
    len_r, offset = parse_element(hex_sig, offset, 2)
    len_r_int = int(len_r, 16) * 2   # Each byte represents 2 characters
    r, offset = parse_element(hex_sig, offset, len_r_int)
    # Get s
    marker, offset = parse_element(hex_sig, offset, 2)
    assert marker == '02', "Wrong s marker."
    len_s, offset = parse_element(hex_sig, offset, 2)
    len_s_int = int(len_s, 16) * 2  # Each byte represents 2 characters
    s, offset = parse_element(hex_sig, offset, len_s_int)
    # Get ht
    ht, offset = parse_element(hex_sig, offset, 2)
    assert offset == len(hex_sig), "Wrong parsing."

    return r, s, ht


example_sig = None  # insert_sig_here
r, s, ht = dissect_signature(example_sig)
print "r: %s\ns: %s\nht: %s\n" % (r, s, ht)
  • Very helpful! Can I ask where you got your diagram? Might be a paper i'd be interested in reading – Malone Mar 27 '18 at 7:24
  • 1
    eprint.iacr.org/2016/1184.pdf – sr-gi Mar 27 '18 at 8:31
  • @sr-gi are you able to provide code for this? – GK89 Nov 24 '18 at 18:10
  • 1
    @GK89 I've included the code – sr-gi Nov 28 '18 at 11:46
2

Example: https://blockchain.info/tx/463b93f613da09b51d692f48674137f303050e4a5f2cc60ebf349b3c45e192d6

First "Signature" (sans the public key) which contains the R and S values is:

304402206878b5690514437a2342405029426cc2b25b4a03fc396fef845d656cf62bad2c022018610a8d37e3384245176ab49ddbdbe8da4133f661bf5ea7ad4e3d2b912d856f01

This breaks down into:

30

44

02

20

6878b5690514437a2342405029426cc2b25b4a03fc396fef845d656cf62bad2c

02

20

18610a8d37e3384245176ab49ddbdbe8da4133f661bf5ea7ad4e3d2b912d856f

01

The 30, I think, is standard.

The 44 is the number of bytes that will be taken up by, R, S, and their preceding numbers. 44 in hex is 68 in decimal form. Thus referencing that after this point until (but not including) the 01 there will be 68 bytes of data or 136 alpha numeric characters.

The 02 is a number which identifies the following value (in this case, R) as an integer (I think)

The 20 is the number which identifies the number of bytes (or number of hex characters/numbers times 2) of the following value (in this case, R). This value is in hex (ie: 20 in hex is 32 in decimal, signifying 32 bytes or 64 alpha/numeric characters)

The 6878b5690514437a2342405029426cc2b25b4a03fc396fef845d656cf62bad2c is the actual "R" value referenced by the preceding 0220.

The second 02 identifies the following value as an integer (in this case, S).

The second 20 is the number which identifies the number of bytes (or number of hex characters/numbers times 2) of the following value (in this case, S). This value is in hex (ie: 20 in hex is 32 in decimal, signifying 32 bytes or 64 alpha/numeric characters)

The 18610a8d37e3384245176ab49ddbdbe8da4133f661bf5ea7ad4e3d2b912d856f is the "S" value referenced by the preceding 0220.

I think the 01 is merely a reference as to the end of this part of the transaction data.

Some R and S values may be different lengths, the preceding numbers will tell you how long they are.

Information for additional reference:

R = 47253809947851177065887724633329625063088643784040492056218945870752194997548

S = 11026965355983493404719379810734327200902731292741433431270495068542334764399

The Second Input in this Transaction

304402205473f7d4c042bcada7ab63d3d9997bb7945353d388abbea2435d6536c84dca9b0220635f3c3660c375f34a8101b4040b8e046749e8b8517439b090b34bd14b41388301

Breaks down to the following

30

44

02

20

5473f7d4c042bcada7ab63d3d9997bb7945353d388abbea2435d6536c84dca9b

02

20

635f3c3660c375f34a8101b4040b8e046749e8b8517439b090b34bd14b413883

01

To reference your comment in your question

In the first part of the example transaction I showed, to rip the R value from the data, you would have to remove the first 3 bytes (or the 304402, aka the first 6 individual numbers). Then you would have to convert the subsequent first byte (or 2 digit number) being 20. You would then have to convert this into decimal (which would be 32). Then erase the 20 and then read ONLY the next 32 bytes (aka the "R" value), which could also be described as reading the next 64 alphanumeric characters. You could then start the whole thing over again and shift the values over to identify the S value instead of the R value.

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