Switch all EC and ECDSA logic from num to scalar. #117

1. 
   sipa commented at 7:46 pm on November 26, 2014: contributor

   This contains several commits, first some that introduce new functionality (and tests) for scalar, and then several steps of switching the actual logic from secp256k1_num_t based operations to secp256k1_scalar_t based one. For initialization, modular inverses, lambda splitting and tests, the num module is still used for now.
2. 
   sipa commented at 7:47 pm on November 26, 2014: contributor

   Oh, it’s also a tiny bit faster, it seems…
3. sipa force-pushed on Nov 26, 2014
4. 
   gmaxwell commented at 0:57 am on November 27, 2014: contributor

   I have my fuzz testing running on this now. So far, so good, at least it passes all the test cases I previously generated.
5. sipa force-pushed on Nov 27, 2014
6. sipa cross-referenced this on Nov 28, 2014 from issue Make the num module optional by sipa
7. sipa force-pushed on Nov 30, 2014
8. sipa force-pushed on Nov 30, 2014
9. Add secp256k1_scalar_add_bit 5213207856
10. Generalize secp256k1_scalar_get_bits 1e6c77c321
11. Switch wnaf splitting from num-based to scalar-based 0b73059709
12. Make test_point_times_order test meaningful again

    As wnaf splitting is scalar based, multiplying with the order directly
    would be reduced to multiplication with zero before even converting to
    wnaf.

    b5c9ee756f
13. Add secp256k1_scalar_inverse_var which delegates to GMP d1502eb459
14. Add scalar splitting functions

    Which currently delegate to the lambda-splitter in group.

    6794be6080
15. Switch all EC/ECDSA logic from num to scalar f24041d6aa
16. Move lambda-splitting code to scalar.

    It's not really an operation on group elements.

    4285a98722
17. Remove unused num functions c76be9efa0
18. sipa force-pushed on Nov 30, 2014
19. 
    gmaxwell commented at 9:31 am on December 1, 2014: contributor

    ACK.
20. sipa merged this on Dec 1, 2014
21. sipa closed this on Dec 1, 2014

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22. sipa referenced this in commit e2e8a362ad on Dec 1, 2014

Contributors
sipa gmaxwell