Twice faster Jacobian quotients #13
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This makes FromJacToJac about 50% faster, mostly from avoiding switching rings and variable substitutions, and computing manually the expansion as symmetric functions.
The polynomial argument is no longer an element of the fraction field.
The point is already known to be of order 3 so providing information to the constructor avoids unnecessary work.
The cost of apply the Richelot isogeny determines how many precomputed Jacobian point powers are worth keeping between FromJacToJac iterations. Since the image computation is now twice faster, we can pass around a second precomputed power to keep balance.
This allows for minor simplifications and is about 10% faster.
SAGE monic() method on polynomials is very generic and often slow due to going through many layers of Python objects. It turns out that all Jacobian doubling formulas are also compatible with non-monic Mumford coordinates so relaxing that constraint saves some operations and accelerates computation by about 10%.
Looking carefully at the coefficients of polynomials H1,H2,H3 they turn out to be almost exactly the coefficients of the inverse matrix. This removes some redundant computations as the determinant computation needs very similar operations.
Initialisation of isogenies in SAGE is much faster when using points as arguments rather than polynomials. On SIKE_challenge this is a 10%-15% speedup.
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This series of changes removes some unnecessary or redundant computations leading to a 2x speedup overall.
Before:
sage SIKE_challenge.sage 281.15s user 0.39s system 99% cpu 4:42.12 total
After:
sage SIKE_challenge.sage 106.24s user 0.25s system 100% cpu 1:46.46 total