Optimization of G2 subgroup check using NAF representation #266
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The table below presents the gas usage reports for the
As observed, there appears to be a slight regression in performance with these changes compared to the implementation of the |
chfast
reviewed
Jun 11, 2024
| // naf digit = -1 | ||
| if and(naf, 2) { | ||
| let pn00, pn01, pn10, pn11, pn20, pn21 := g2JacobianNeg(p00, p01, p10, p11, p20, p21) | ||
| q00, q01, q10, q11, q20, q21 := g2JacobianAdd(q00, q01, q10, q11, q20, q21, pn00, pn01, pn10, pn11, pn20, pn21) |
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You may have better performance if iterating X_NAF from MSB to LSB. Then you add either constant P or constant -P and the later can be computed once.
Here is snippet from wikipedia:
let bits = bit_representation(s) # the vector of bits (from LSB to MSB) representing s
let i = length(bits) - 2
let res = P
while (i >= 0): # traversing from second MSB to LSB
res = res + res # double
if bits[i] == 1:
res = res + P # add
i = i - 1
return res
| function X_NAF() -> ret { | ||
| // NAF in binary form | ||
| // 010000000100010000100001000100100000010001001000100010000100000001000001000100010010000100000100000000010001000000001000000001 | ||
| ret := 21356084665891114007971320526050427393 |
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This closes #237.