| Commit message (Collapse) | Author | Age |
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Experiments/SpecEd25519 will come back soon
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This should allow a nice elegant abstract way of doing bounds analysis.
It's possible that wf should be redefined in terms of rel_wf.
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Quoting Andres:
> I am leaning towards putting this in Specifc instead of Experiments -- it
> seems like complete result on its own, these files are unlikely to be reused
> for something else, and I don't think we are expecting to need to remove it
> any time soon. Currently, `Specific` code does not quantify over anything (no
> context variables), but this seems secondary. We could make versions of this
> with the curve constants plugged in, though.
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After | File Name | Before || Change
------------------------------------------------------------------------
0m12.69s | Total | 0m00.00s || +0m12.69s
------------------------------------------------------------------------
0m06.96s | Experiments/FancyMachineMontgomery256 | N/A || +0m06.96s
0m03.07s | Experiments/FancyMachineBarrett256 | N/A || +0m03.06s
0m02.67s | Experiments/FancyMachine256 | N/A || +0m02.67s
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The proof of wf-preservation for inline_const isn't finished yet, though...
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It's probably not going to be used
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This method allows a proof term that's linear in the term being proven
well-founded, rather than exponential in it. By factoring out all of the
reasoning about expressions, we can incur overhead equal to (the number of
constants) + (the number of let-bindings) + (the number of variables used), all
without mentioning the term itself; [vm_compute] can do the appropriate
reduction for us.
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We also have linearization of function application / lets,
constant-inlining, and reification.
This closes #58.
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Now the rewrite strategy no longer relies on projections of anything
other than [decode], and the conversion to ZLike is simpler.
Modulo some annoyingly delicate arithmetic around things like [2^n * 2^n
= 2^(2*n)] and whether to factor [(decode (fst x) + decode (snd x) >> n)
>> b] as [decode x >> n] or as [shrd (fst x) (snd x) n], the proofs
bascially go by pulling/pushing decodes.
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ModularBaseSystem are now in ModularBaseSystemProofs.v and Specific/
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This provides a cleaner interface for the bottom level implementation,
as well as an implementation of multiplying 128x128 -> 256.
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Also use it to implement Montgomery reduction and Barrett reduction.
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This is partly done for my own benefit, to internalize how Montgomery
multiplication works, and partly done as a template for word-based
Montgomery multiplication when the carrying does not take advantage of
the fact that we are using a pseudomersenne prime.
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From http://cacr.uwaterloo.ca/hac/about/chap14.pdf
This should take care of most of #43, at least the specification on Z
part of it.
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In this version, we split up the integer division so that we are less
likely to overflow in intermediate computations.
This is still not the version in HAC 14.42; that version also does early
reduction modulo b^(k+1).
This is work towards #43
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After | File Name | Before || Change
----------------------------------------------------------------------------------
1m43.58s | Total | 1m44.69s || -0m01.10s
----------------------------------------------------------------------------------
0m32.94s | Specific/GF25519 | 0m33.18s || -0m00.24s
0m15.34s | ModularArithmetic/ModularBaseSystemProofs | 0m15.35s || -0m00.00s
0m11.42s | Experiments/SpecEd25519 | 0m11.46s || -0m00.04s
0m07.12s | Specific/GF1305 | 0m07.38s || -0m00.25s
0m04.04s | ModularArithmetic/Pow2BaseProofs | 0m04.09s || -0m00.04s
0m03.82s | ModularArithmetic/Tutorial | 0m03.79s || +0m00.02s
0m03.81s | BaseSystemProofs | 0m03.71s || +0m00.10s
0m03.16s | ModularArithmetic/ModularBaseSystemOpt | 0m03.23s || -0m00.06s
0m02.76s | Util/ZUtil | 0m02.79s || -0m00.03s
0m01.63s | ModularArithmetic/PrimeFieldTheorems | 0m01.65s || -0m00.02s
0m01.58s | Encoding/PointEncodingPre | 0m01.51s || +0m00.07s
0m01.57s | ModularArithmetic/ModularArithmeticTheorems | 0m01.59s || -0m00.02s
0m01.33s | BaseSystem | 0m01.50s || -0m00.16s
0m01.09s | ModularArithmetic/ExtendedBaseVector | 0m01.13s || -0m00.03s
0m00.95s | Experiments/DerivationsOptionRectLetInEncoding | 0m00.97s || -0m00.02s
0m00.93s | ModularArithmetic/BarrettReduction/Z | 0m00.98s || -0m00.04s
0m00.91s | Util/NumTheoryUtil | 0m01.19s || -0m00.27s
0m00.91s | ModularArithmetic/ModularBaseSystemField | 0m00.91s || +0m00.00s
0m00.81s | ModularArithmetic/ModularBaseSystemListProofs | 0m00.81s || +0m00.00s
0m00.74s | Experiments/SpecificCurve25519 | 0m00.70s || +0m00.04s
0m00.65s | Encoding/ModularWordEncodingTheorems | 0m00.72s || -0m00.06s
0m00.65s | Encoding/ModularWordEncodingPre | 0m00.62s || +0m00.03s
0m00.64s | Testbit | 0m00.66s || -0m00.02s
0m00.63s | ModularArithmetic/ExtPow2BaseMulProofs | 0m00.63s || +0m00.00s
0m00.63s | Spec/ModularWordEncoding | 0m00.63s || +0m00.00s
0m00.60s | ModularArithmetic/ModularBaseSystem | 0m00.57s || +0m00.03s
0m00.59s | ModularArithmetic/ModularBaseSystemList | 0m00.61s || -0m00.02s
0m00.57s | ModularArithmetic/PseudoMersenneBaseParamProofs | 0m00.61s || -0m00.04s
0m00.56s | ModularArithmetic/Pre | 0m00.48s || +0m00.08s
0m00.41s | ModularArithmetic/Pow2Base | 0m00.42s || -0m00.01s
0m00.38s | ModularArithmetic/PseudoMersenneBaseParams | 0m00.43s || -0m00.04s
0m00.38s | Spec/ModularArithmetic | 0m00.39s || -0m00.01s
0m00.04s | Util/Bool | N/A || +0m00.04s
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I do hereby revoke the privilege of [intuition] to grab random hints
from random databases. This privilege is reserved for
[debug_intuition], which comes with a warning about not being used in
production code. This tactic is useful in conjunction with `Print Hint
*`, to discover what hint databases the hints were grabbed from.
(Suggestions for renaming [debug_intuition] welcome.)
Any file using [intuition] must [Require Export
Crypto.Util.FixCoqMistakes.]. It's possible we could lift this
restriction by compiling [FixCoqMistakes] separately, and passing along
`-require FixCoqMistakes` to Coq. Should we do this?
After | File Name | Before || Change
------------------------------------------------------------------------------------
3m29.54s | Total | 4m33.13s || -1m03.59s
------------------------------------------------------------------------------------
0m03.75s | BaseSystemProofs | 0m43.84s || -0m40.09s
0m42.57s | CompleteEdwardsCurve/ExtendedCoordinates | 0m34.48s || +0m08.09s
0m03.04s | Util/ListUtil | 0m11.18s || -0m08.14s
0m01.62s | ModularArithmetic/PrimeFieldTheorems | 0m09.53s || -0m07.90s
0m00.87s | Util/NumTheoryUtil | 0m07.61s || -0m06.74s
0m01.61s | Encoding/PointEncodingPre | 0m06.93s || -0m05.31s
0m51.95s | Specific/GF25519 | 0m47.52s || +0m04.42s
0m12.30s | Experiments/SpecEd25519 | 0m11.29s || +0m01.01s
0m09.22s | Specific/GF1305 | 0m08.17s || +0m01.05s
0m03.48s | CompleteEdwardsCurve/Pre | 0m04.77s || -0m01.28s
0m02.70s | Assembly/State | 0m04.09s || -0m01.38s
0m01.55s | ModularArithmetic/ModularArithmeticTheorems | 0m02.93s || -0m01.38s
0m01.16s | Assembly/Pseudize | 0m02.34s || -0m01.17s
0m15.67s | CompleteEdwardsCurve/CompleteEdwardsCurveTheorems | 0m16.37s || -0m00.70s
0m06.02s | Algebra | 0m06.67s || -0m00.65s
0m05.90s | Experiments/GenericFieldPow | 0m06.68s || -0m00.77s
0m04.65s | WeierstrassCurve/Pre | 0m05.27s || -0m00.61s
0m03.93s | ModularArithmetic/Pow2BaseProofs | 0m03.94s || -0m00.00s
0m03.70s | ModularArithmetic/Tutorial | 0m03.85s || -0m00.14s
0m02.83s | ModularArithmetic/ModularBaseSystemOpt | 0m02.84s || -0m00.00s
0m02.74s | Experiments/EdDSARefinement | 0m01.80s || +0m00.94s
0m02.35s | Util/ZUtil | 0m02.51s || -0m00.15s
0m01.86s | Assembly/Wordize | 0m02.32s || -0m00.45s
0m01.23s | ModularArithmetic/ExtendedBaseVector | 0m01.20s || +0m00.03s
0m01.21s | BaseSystem | 0m01.63s || -0m00.41s
0m01.03s | Experiments/SpecificCurve25519 | 0m00.98s || +0m00.05s
0m01.01s | ModularArithmetic/ModularBaseSystemProofs | 0m01.11s || -0m00.10s
0m00.95s | ModularArithmetic/BarrettReduction/Z | 0m01.38s || -0m00.42s
0m00.92s | Experiments/DerivationsOptionRectLetInEncoding | 0m01.81s || -0m00.89s
0m00.85s | ModularArithmetic/ModularBaseSystemField | 0m00.86s || -0m00.01s
0m00.82s | ModularArithmetic/ModularBaseSystemListProofs | 0m00.79s || +0m00.02s
0m00.80s | Assembly/QhasmEvalCommon | 0m00.93s || -0m00.13s
0m00.73s | Spec/EdDSA | 0m00.59s || +0m00.14s
0m00.72s | Util/Tuple | 0m00.71s || +0m00.01s
0m00.70s | Util/IterAssocOp | 0m00.72s || -0m00.02s
0m00.67s | Encoding/ModularWordEncodingTheorems | 0m00.71s || -0m00.03s
0m00.66s | Assembly/Pipeline | 0m00.64s || +0m00.02s
0m00.65s | Testbit | 0m00.65s || +0m00.00s
0m00.65s | Assembly/PseudoConversion | 0m00.65s || +0m00.00s
0m00.64s | Util/AdditionChainExponentiation | 0m00.63s || +0m00.01s
0m00.63s | ModularArithmetic/ExtPow2BaseMulProofs | 0m00.64s || -0m00.01s
0m00.63s | Assembly/Pseudo | 0m00.65s || -0m00.02s
0m00.62s | ModularArithmetic/ModularBaseSystem | 0m00.57s || +0m00.05s
0m00.61s | ModularArithmetic/ModularBaseSystemList | 0m00.57s || +0m00.04s
0m00.60s | Encoding/ModularWordEncodingPre | 0m00.69s || -0m00.08s
0m00.60s | ModularArithmetic/PseudoMersenneBaseParamProofs | 0m00.59s || +0m00.01s
0m00.56s | Assembly/StringConversion | 0m00.56s || +0m00.00s
0m00.54s | Spec/ModularWordEncoding | 0m00.61s || -0m00.06s
0m00.54s | Assembly/QhasmUtil | 0m00.46s || +0m00.08s
0m00.52s | Assembly/Qhasm | 0m00.53s || -0m00.01s
0m00.48s | Assembly/AlmostQhasm | 0m00.52s || -0m00.04s
0m00.48s | ModularArithmetic/Pre | 0m00.48s || +0m00.00s
0m00.46s | Assembly/Vectorize | 0m00.72s || -0m00.25s
0m00.45s | Spec/WeierstrassCurve | 0m00.44s || +0m00.01s
0m00.44s | Assembly/AlmostConversion | 0m00.44s || +0m00.00s
0m00.43s | ModularArithmetic/Pow2Base | 0m00.51s || -0m00.08s
0m00.42s | ModularArithmetic/PseudoMersenneBaseParams | 0m00.38s || +0m00.03s
0m00.41s | Spec/CompleteEdwardsCurve | 0m00.43s || -0m00.02s
0m00.34s | Spec/ModularArithmetic | 0m00.36s || -0m00.01s
0m00.03s | Util/FixCoqMistakes | N/A || +0m00.03s
0m00.02s | Util/Notations | 0m00.04s || -0m00.02s
0m00.02s | Util/Tactics | 0m00.02s || +0m00.00s
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organization of reasoning.
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ModularBaseSystem is fully defined, rather than after ModularBaseSystemOpt
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defined conversion between two such bases. This will allow conversion between the pseudomersenne base representation and the wire format. Also relocated some lemmas to Util.
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Define the spec of Weierstrass curves
This is the start of work on P256.
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Implement and prove Barrett reduction on Z
This will serve as the high-level algorithm for modular reduction.
We follow Wikipedia very closely, except where we can do better (I
believe @jadephilipoom is updating Wikipedia).
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