diff options
| author |  jadep <jade.philipoom@gmail.com> | 2017-01-09 11:24:40 -0500 |
|---|---|---|
| committer | jadep <jade.philipoom@gmail.com> | 2017-01-09 11:24:46 -0500 |
| commit | ba8cc0116195fe3010a0f8ffd0e5d89618431a0c (patch) | |
| tree | ac4b4040c87adf64636190f3f6b91a04e9c23eb4 /optimizations.md | |
| parent | b15ea968f12019f84538b74df09bf4be48886866 (diff) | |
optimizations.md: add missing descriptions and Karatsuba's trick
Diffstat (limited to 'optimizations.md')
| -rw-r--r-- | optimizations.md | 7 |
1 files changed, 3 insertions, 4 deletions
diff --git a/optimizations.md b/optimizations.md index cf9c9fe89..099dd670a 100644 --- a/optimizations.md +++ b/optimizations.md @@ -3,11 +3,10 @@ | Field Arithmetic | Unsaturated limbs/delayed carrying | Implemented | [ModularBaseSystemProofs.v#L347](https://github.com/mit-plv/fiat-crypto/blob/master/src/ModularArithmetic/ModularBaseSystemProofs.v#L347) | Represent field elements using more machine words than strictly necessary in order to delay carrying (for example, represent a 255-bit number using 51 bits per 64-bit word) | | Field Arithmetic | Division-free Modular Reduction | Implemented | [PseudoMersenneBaseParamProofs.v#L41](https://github.com/mit-plv/fiat-crypto/blob/master/src/ModularArithmetic/PseudoMersenneBaseParamProofs.v#L41) | Reduce $x$ modulo $2^k-c$ by splitting $x$ into $a$ and $b$ such that $a + 2^k * b = x$, then returning $a + c * b$ | | Field Arithmetic | Inverse square root | Not Implemented | n/a | Compute $\frac{1}{\sqrt{x}}$ rather than $\sqrt{x}$. Then, for example, in order to compute $\sqrt{\frac{x}{y}}$, compute $x * \frac{1}{\sqrt{xy}}$ rather than doing two expensive square root computations | -| Field Arithmetic | Hex Exponentiation | Not Implemented | n/a | TODO | +| Field Arithmetic | Hex Exponentiation | Not Implemented | n/a | Use hexadecimal exponentiation for elliptic curve scalar multiplication | | Field Arithmetic | Addition Chain Exponentiation | Implemented | [AdditionChainExponentiation.v#L53](https://github.com/mit-plv/fiat-crypto/blob/master/src/Util/AdditionChainExponentiation.v#L53) | https://en.wikipedia.org/wiki/Addition-chain_exponentiation | -| Field Arithmetic | Precomputed Tables | Not Implemented | n/a | TODO | +| Field Arithmetic | Precomputed Tables | Not Implemented | n/a | Precompute powers of base point | | Elliptic Curve Points | Extended Coordinates | Implemented | [ExtendedCoordinates.v#L258](https://github.com/mit-plv/fiat-crypto/blob/master/src/CompleteEdwardsCurve/ExtendedCoordinates.v#L258) | http://hyperelliptic.org/EFD/g1p/auto-edwards.html | +| Field Arithmetic | Karatsuba | Not Implemented | n/a | Use Karatsuba's trick for multiplication (mostly relevant for primes $> 400$ bits in size) | | Elliptic Curve Points | Point Compression | Implemented | [PointEncodingPre.v#L313](https://github.com/mit-plv/fiat-crypto/blob/master/src/Encoding/PointEncodingPre.v#L313) and [PointEncodingPre.v#L412](https://github.com/mit-plv/fiat-crypto/blob/master/src/Encoding/PointEncodingPre.v#L412) | Instead of transmitting $(x,y)$ to transmit a point, transmit $y$ and a bit representing the sign of $x$. Decode $x$ by solving the curve equation for $x^2$, taking the square root, and picking the square root with the appropriate sign bit | | Low-Level | Use Varied-size Registers | Half-Implemented | [MapCastWithCastOp.v#L116](https://github.com/mit-plv/fiat-crypto/blob/master/src/Reflection/MapCastWithCastOp.v#L116) | Rather than using the largest available integer size (e.g., `uint32_t` on x86_32, `uint64_t` on x86_64) for all operations, pick the smallest integer size which is guaranteed to fit the result for each arithmetic operation separately | - - |