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Document PRAC rule conditions

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Miguel Oliveira 2022-12-13 18:40:52 -03:00
parent d4c173c713
commit 08016b8a61
1 changed files with 16 additions and 12 deletions
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28
internal/fq.lua
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@ -255,8 +255,12 @@ end
--- Makes a PRAC ruleset from a pair of scalars. --- Makes a PRAC ruleset from a pair of scalars.
-- --
-- @tparam {number...} a A scalar a < q as 11 limbs in [0..2²⁴). -- For more information see section 3.3 of Speeding up subgroup cryptosystems:
-- @tparam {number...} b A scalar b < q as 11 limbs in [0..2²⁴). -- Martijn Stam. Speeding up subgroup cryptosystems. PhD thesis, Technische
-- Universiteit Eindhoven, 2003. https://dx.doi.org/10.6100/IR564670.
--
-- @tparam {number...} a A scalar 2²⁶⁴ × a mod q as 11 limbs in [0..2²⁴).
-- @tparam {number...} b A scalar 2²⁶⁴ × b mod q as 11 limbs in [0..2²⁴).
-- @treturn {{number...}, {number...}} The generated ruleset. -- @treturn {{number...}, {number...}} The generated ruleset.
-- --
local function makeRuleset(a, b) local function makeRuleset(a, b)
@ -283,7 +287,7 @@ local function makeRuleset(a, b)
local rules = {} local rules = {}
while ff ~= 0 do while ff ~= 0 do
if ff < 0 then if ff < 0 then
-- M0. -- M0. d < e
rules[#rules + 1] = 0 rules[#rules + 1] = 0
-- (d, e) ← (e, d) -- (d, e) ← (e, d)
dt, et = et, dt dt, et = et, dt
@ -293,7 +297,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = -ff ff = -ff
elseif 4 * ff < ef and d3 == lut3[e3] then elseif 4 * ff < ef and d3 == lut3[e3] then
-- M1. -- M1. e < d ≤ 5/4 e, d ≡ -e (mod 3)
rules[#rules + 1] = 1 rules[#rules + 1] = 1
-- (d, e) ← ((2d - e)/3, (2e - d)/3) -- (d, e) ← ((2d - e)/3, (2e - d)/3)
dt, et = mp.third(mp.add(dt, ft)), mp.third(mp.sub(et, ft)) dt, et = mp.third(mp.add(dt, ft)), mp.third(mp.sub(et, ft))
@ -301,7 +305,7 @@ local function makeRuleset(a, b)
d3, e3 = mp.mod3(dt), mp.mod3(et) d3, e3 = mp.mod3(dt), mp.mod3(et)
ef = mp.approx(et) ef = mp.approx(et)
elseif 4 * ff < ef and d2 == e2 and d3 == e3 then elseif 4 * ff < ef and d2 == e2 and d3 == e3 then
-- M2. -- M2. e < d ≤ 5/4 e, d ≡ e (mod 6)
rules[#rules + 1] = 2 rules[#rules + 1] = 2
-- (d, e) ← ((d - e)/2, e) -- (d, e) ← ((d - e)/2, e)
dt = mp.half(ft) dt = mp.half(ft)
@ -310,7 +314,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif ff < 3 * ef then elseif ff < 3 * ef then
-- M3. -- M3. d ≤ 4e
rules[#rules + 1] = 3 rules[#rules + 1] = 3
-- (d, e) ← (d - e, e) -- (d, e) ← (d - e, e)
dt = mp.carryWeak(ft) dt = mp.carryWeak(ft)
@ -319,7 +323,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif d2 == e2 then elseif d2 == e2 then
-- M4 (same as M2). -- M4. d ≡ e (mod 2)
rules[#rules + 1] = 2 rules[#rules + 1] = 2
-- (d, e) ← ((d - e)/2, e) -- (d, e) ← ((d - e)/2, e)
dt = mp.half(ft) dt = mp.half(ft)
@ -328,7 +332,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif d2 == 0 then elseif d2 == 0 then
-- M5. -- M5. d ≡ 0 (mod 2)
rules[#rules + 1] = 5 rules[#rules + 1] = 5
-- (d, e) ← (d/2, e) -- (d, e) ← (d/2, e)
dt = mp.half(dt) dt = mp.half(dt)
@ -337,7 +341,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif d3 == 0 then elseif d3 == 0 then
-- M6. -- M6. d ≡ 0 (mod 3)
rules[#rules + 1] = 6 rules[#rules + 1] = 6
-- (d, e) ← (d/3 - e, e) -- (d, e) ← (d/3 - e, e)
dt = mp.carryWeak(mp.sub(mp.third(dt), et)) dt = mp.carryWeak(mp.sub(mp.third(dt), et))
@ -346,7 +350,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif d3 == lut3[e3] then elseif d3 == lut3[e3] then
-- M7. -- M7. d ≡ -e (mod 3)
rules[#rules + 1] = 7 rules[#rules + 1] = 7
-- (d, e) ← ((d - 2e)/3, e) -- (d, e) ← ((d - 2e)/3, e)
dt = mp.third(mp.sub(ft, et)) dt = mp.third(mp.sub(ft, et))
@ -354,7 +358,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
elseif d3 == e3 then elseif d3 == e3 then
-- M8. -- M8. d ≡ e (mod 3)
rules[#rules + 1] = 8 rules[#rules + 1] = 8
-- (d, e) ← ((d - e)/3, e) -- (d, e) ← ((d - e)/3, e)
dt = mp.third(ft) dt = mp.third(ft)
@ -363,7 +367,7 @@ local function makeRuleset(a, b)
ft = mp.sub(dt, et) ft = mp.sub(dt, et)
ff = mp.approx(ft) ff = mp.approx(ft)
else else
-- M9. -- M9. e ≡ 0 (mod 2)
rules[#rules + 1] = 9 rules[#rules + 1] = 9
-- (d, e) ← (d, e/2) -- (d, e) ← (d, e/2)
et = mp.half(et) et = mp.half(et)