2

I have a conceptual understanding of the R value in so far as it can fall either above or below the X axis in the elliptical curve and that positive R values use an extra byte in the signature to indicate that they are in fact positive R values. I am trying to look at transactions to try and get my head around this in practice. For example:

TXID: 4a8f2d489008f60c7d02526b5f264ae70c465e1ea4fe710243f04ca6b1e3b103

ScriptSig:
OP_PUSHBYTES_71 304402200222918fd7512cd5ecbdfda82dd48cb57677b5b6d42e17b5505fe2f2873d9651022032aab83fece0a48a338e8c003e2907fcd3d2a8798f16ddb5b206351452189cee01
OP_PUSHBYTES_33 034607e699d21f3a4b0c0523869eb185ba23a40a2ffaefe1c567b3b7a6eeb43026

Versus

TXID: 4247bbae1e7d08ed31aee8fc1f65bf4dc7411fe7ff5f64d2d7d0f4ad3117c148

ScriptSig
OP_PUSHBYTES_72 3045022100ba76172000fa3c943a714b1152dc370060805b1cc8cbbd466710325e5874bfc002203e57b406e6af2f52ded43a45bfcb8402acff88f752a5806612bbbc3e80c49c1601
OP_PUSHBYTES_33 023ac3778b0e613501c0469c3232a0b3ff62e53b9849c891c446c44cffa74dd8ce

Does this mean that because the signature is only 71 bytes in the first transaction (as opposed to 72 in the second) that the R value for the first signature would be negative?

Improve this question

1 Answer 1

Reset to default
2

In DER-encoded signatures, the r and s values need to be prepended with 0x00 only if they start with the byte 0x80 or higher (i.e. have their first bit set). The r-value of the first signature starts with 0x02, so it doesn't need the extra byte.

This is unrelated to elliptic curve points falling above or below the X axis because 1. point coordinates on the secp256k1 curve are integers modulo p so they cannot be negative, and 2. because p is slightly less than 2256 there are r and s values that fall into the upper half of the range but start with the byte 0x79.

Improve this answer
2
  • Clearly the first sentence of my question was a lie - I need to do more study. Given what you mentioned about points on the curve being modulo p therefore they can't be negative, then how do we distinguish points above and below the x axis if not by calling them positive or negative?
    – user2334659
    Commented Mar 7 at 8:13
  • 1
    In elliptic curves over finite fields there simply aren't any points below the X axis. The point coordinates can only take values between 0 (inclusive) and p (exclusive).
    – Vojtěch Strnad
    Commented Mar 14 at 7:29

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.