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Can't find SECP-256k1 description by Gura et al. [2004] + other issues for Appendix F #335

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jamesray1 opened this issue Sep 12, 2017 · 3 comments
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@jamesray1
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jamesray1 commented Sep 12, 2017

Unresolved comments remain:

  • formula 214 equality for secp256k1n is omitted.

I moved most of the original comments to #327 where the changes have been made, except for the below one.

@jamesray1 jamesray1 changed the title Can't find SECP-256k1 description by Gura et al. [2004] Can't find SECP-256k1 description by Gura et al. [2004] + other issues for Appendix F sentence 1 Sep 12, 2017
@jamesray1 jamesray1 changed the title Can't find SECP-256k1 description by Gura et al. [2004] + other issues for Appendix F sentence 1 Can't find SECP-256k1 description by Gura et al. [2004] + other issues for Appendix F Sep 12, 2017
@jamesray1
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jamesray1 commented Sep 12, 2017

For formula 214, secp256k1n= 115792089237316195423570985008687907852837564279074904382605163141518161494337, have a footnote to say that this is FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD036‌ in hexadecimal (which is 78 characters in length, so it is also less than 16^78 = 8.3436994e+93).

I noticed that this line is commented out:
%\mathtt{\tiny secp256k1p} &= 2^{256} - 2^{32} - 977\\
Why omit it? It helps to give an idea of the order of magnitude of the number and a formula for it.
@pirapira

jamesray1 added a commit to jamesray1/yellowpaper that referenced this issue Sep 16, 2017
For the added refs, see ethereum#335
For Appendix F:
- ECDSAWikipedia and ECDSAcerticom for "we assert the functions ECDSASIGN, ECDSARESTORE and ECDSAPUBKEY. These are formally defined in the literature." ethereum#335 (comment)
- secp256k1BitcoinWiki2016 and secp256k1StackExchange2014 for Secp256k1. ethereum#335 (comment)
- npmElectrum2017 for Electrum style signatures. ethereum#335 (comment)
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pirapira commented Sep 20, 2017

This issue contains many points, many of which have materialized into a PR and requires no further discussion here. So it's not trivial to see if anything remains to be answered or discussed here.

Suggestion1: open a new issue for each logically independent issue.

Suggestion2: keep a list of open points in the first comment of the issue

  • the definition of SECP-256k1 is not found in the cited reference
  • ...

@jamesray1
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jamesray1 commented Sep 23, 2017

Ah, I see that:
115 792 089 237 316 195 423 570 985 008 687 907 852 837 564 279 074 904 382 605 163 141 518 161 494 337
is not the same as 2^{256} - 2^{32} - 977.

2^256 - 2^32 - 977 =
115 792 089 237 316 195 423 570 985 008 687 907 853 269 984 665 640 564 039 457 584 007 908 834 671 663.

These leading digits of the two numbers are the same:
115 792 089 237 316 195 423 570 985 008 687 907 85

115 792 089 237 316 195 423 570 985 008 687 907 852 837 564 279 074 904 382 605 163 141 518 161 494 337
is less than 2^256 - 2^32 - 977

jamesray1 added a commit to jamesray1/yellowpaper that referenced this issue Nov 26, 2018
For the added refs, see ethereum#335
For Appendix F:
- ECDSAWikipedia and ECDSAcerticom for "we assert the functions ECDSASIGN, ECDSARESTORE and ECDSAPUBKEY. These are formally defined in the literature." ethereum#335 (comment)
- secp256k1BitcoinWiki2016 and secp256k1StackExchange2014 for Secp256k1. ethereum#335 (comment)
- npmElectrum2017 for Electrum style signatures. ethereum#335 (comment)
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