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Square Root: addition chain for Bandersnatch and banderwagon #356

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Feb 11, 2024
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Square Root: addition chain for Bandersnatch and banderwagon #356

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2 changes: 1 addition & 1 deletion constantine/math/arithmetic/finite_fields.nim
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Expand Up @@ -567,7 +567,7 @@ macro addchain*(fn: untyped): untyped =
var body = newStmtList()

for i, statement in fn[^1]:
statement.expectKind({nnkCommentStmt, nnkVarSection, nnkCall, nnkInfix})
statement.expectKind({nnkCommentStmt, nnkLetSection, nnkVarSection, nnkCall, nnkInfix})

var s = statement.copyNimTree()
if i + 1 != result[^1].len:
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138 changes: 138 additions & 0 deletions constantine/math/constants/bandersnatch_sqrt.nim
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Expand Up @@ -17,3 +17,141 @@ const
Bandersnatch_TonelliShanks_exponent* = BigInt[222].fromHex"0x39f6d3a994cebea4199cec0404d0ec02a9ded2017fff2dff7fffffff"
Bandersnatch_TonelliShanks_twoAdicity* = 32
Bandersnatch_TonelliShanks_root_of_unity* = Fp[Bandersnatch].fromHex"0x212d79e5b416b6f0fd56dc8d168d6c0c4024ff270b3e0941b788f500b912f1f"

# ############################################################
#
# Specialized Tonelli-Shanks for Bandersnatch
#
# ############################################################

func precompute_tonelli_shanks_addchain*(
r: var Fp[Bandersnatch],
a: Fp[Bandersnatch]) {.addchain.} =
## Does a^Bandersnatch_TonelliShanks_exponent
## via an addition-chain

var
x10 {.noInit.}: Fp[Bandersnatch]
x100 {.noInit.}: Fp[Bandersnatch]
x110 {.noInit.}: Fp[Bandersnatch]
x1100 {.noInit.}: Fp[Bandersnatch]
x10010 {.noInit.}: Fp[Bandersnatch]
x10011 {.noInit.}: Fp[Bandersnatch]
x10110 {.noInit.}: Fp[Bandersnatch]
x11000 {.noInit.}: Fp[Bandersnatch]
x11010 {.noInit.}: Fp[Bandersnatch]
x100010 {.noInit.}: Fp[Bandersnatch]
x110101 {.noInit.}: Fp[Bandersnatch]
x111011 {.noInit.}: Fp[Bandersnatch]
x1001011 {.noInit.}: Fp[Bandersnatch]
x1001101 {.noInit.}: Fp[Bandersnatch]
x1010101 {.noInit.}: Fp[Bandersnatch]
x1100111 {.noInit.}: Fp[Bandersnatch]
x1101001 {.noInit.}: Fp[Bandersnatch]
x10000011 {.noInit.}: Fp[Bandersnatch]
x10011001 {.noInit.}: Fp[Bandersnatch]
x10011101 {.noInit.}: Fp[Bandersnatch]
x10111111 {.noInit.}: Fp[Bandersnatch]
x11010111 {.noInit.}: Fp[Bandersnatch]
x11011011 {.noInit.}: Fp[Bandersnatch]
x11100111 {.noInit.}: Fp[Bandersnatch]
x11101111 {.noInit.}: Fp[Bandersnatch]
x11111111 {.noInit.}: Fp[Bandersnatch]

x10 .square(a)
x100 .square(x10)
x110 .prod(x10, x100)
x1100 .square(x110)
x10010 .prod(x110, x1100)
x10011 .prod(a, x10010)
x10110 .prod(x100, x10010)
x11000 .prod(x10, x10110)
x11010 .prod(x10, x11000)
x100010 .prod(x1100, x10110)
x110101 .prod(x10011, x100010)
x111011 .prod(x110, x110101)
x1001011 .prod(x10110, x110101)
x1001101 .prod(x10, x1001011)
x1010101 .prod(x11010, x111011)
x1100111 .prod(x10010, x1010101)
x1101001 .prod(x10, x1100111)
x10000011 .prod(x11010, x1101001)
x10011001 .prod(x10110, x10000011)
x10011101 .prod(x100, x10011001)
x10111111 .prod(x100010, x10011101)
x11010111 .prod(x11000, x10111111)
x11011011 .prod(x100, x11010111)
x11100111 .prod(x1100, x11011011)
x11101111 .prod(x11000, x11010111)
x11111111 .prod(x11000, x11100111)
# 26 operations

let a = a # Allow aliasing between r and a

# 26+28 = 54 operations
r.square_repeated(x11100111, 8)
r *= x11011011
r.square_repeated(9)
r *= x10011101
r.square_repeated(9)

# 54 + 20 = 74 operations
r *= x10011001
r.square_repeated(9)
r *= x10011001
r.square_repeated(8)
r *= x11010111

# 74 + 27 = 101 operations
r.square_repeated(6)
r *= x110101
r.square_repeated(10)
r *= x10000011
r.square_repeated(9)

# 101 + 19 = 120 operations
r *= x1100111
r.square_repeated(8)
r *= x111011
r.square_repeated(8)
r *= a

# 120 + 41 = 160 operations
r.square_repeated(14)
r *= x1001101
r.square_repeated(10)
r *= x111011
r.square_repeated(15)

# 161 + 21 = 182 operations
r *= x1010101
r.square_repeated(10)
r *= x11101111
r.square_repeated(8)
r *= x1101001

# 182 + 33 = 215 operations
r.square_repeated(16)
r *= x10111111
r.square_repeated(8)
r *= x11111111
r.square_repeated(7)

# 215 + 20 = 235 operations
r *= x1001011
r.square_repeated(9)
r *= x11111111
r.square_repeated(8)
r *= x10111111

# 235 + 26 = 261 operations
r.square_repeated(8)
r *= x11111111
r.square_repeated(8)
r *= x11111111
r.square_repeated(8)

# 261 + 3 = 264 operations
r *= x11111111
r.square()
r *= a
138 changes: 138 additions & 0 deletions constantine/math/constants/banderwagon_sqrt.nim
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Expand Up @@ -17,3 +17,141 @@ const
Banderwagon_TonelliShanks_exponent* = BigInt[222].fromHex"0x39f6d3a994cebea4199cec0404d0ec02a9ded2017fff2dff7fffffff"
Banderwagon_TonelliShanks_twoAdicity* = 32
Banderwagon_TonelliShanks_root_of_unity* = Fp[Banderwagon].fromHex"0x212d79e5b416b6f0fd56dc8d168d6c0c4024ff270b3e0941b788f500b912f1f"

# ############################################################
#
# Specialized Tonelli-Shanks for Banderwagon
#
# ############################################################

func precompute_tonelli_shanks_addchain*(
r: var Fp[Banderwagon],
a: Fp[Banderwagon]) {.addchain.} =
## Does a^Banderwagon_TonelliShanks_exponent
## via an addition-chain

var
x10 {.noInit.}: Fp[Banderwagon]
x100 {.noInit.}: Fp[Banderwagon]
x110 {.noInit.}: Fp[Banderwagon]
x1100 {.noInit.}: Fp[Banderwagon]
x10010 {.noInit.}: Fp[Banderwagon]
x10011 {.noInit.}: Fp[Banderwagon]
x10110 {.noInit.}: Fp[Banderwagon]
x11000 {.noInit.}: Fp[Banderwagon]
x11010 {.noInit.}: Fp[Banderwagon]
x100010 {.noInit.}: Fp[Banderwagon]
x110101 {.noInit.}: Fp[Banderwagon]
x111011 {.noInit.}: Fp[Banderwagon]
x1001011 {.noInit.}: Fp[Banderwagon]
x1001101 {.noInit.}: Fp[Banderwagon]
x1010101 {.noInit.}: Fp[Banderwagon]
x1100111 {.noInit.}: Fp[Banderwagon]
x1101001 {.noInit.}: Fp[Banderwagon]
x10000011 {.noInit.}: Fp[Banderwagon]
x10011001 {.noInit.}: Fp[Banderwagon]
x10011101 {.noInit.}: Fp[Banderwagon]
x10111111 {.noInit.}: Fp[Banderwagon]
x11010111 {.noInit.}: Fp[Banderwagon]
x11011011 {.noInit.}: Fp[Banderwagon]
x11100111 {.noInit.}: Fp[Banderwagon]
x11101111 {.noInit.}: Fp[Banderwagon]
x11111111 {.noInit.}: Fp[Banderwagon]

x10 .square(a)
x100 .square(x10)
x110 .prod(x10, x100)
x1100 .square(x110)
x10010 .prod(x110, x1100)
x10011 .prod(a, x10010)
x10110 .prod(x100, x10010)
x11000 .prod(x10, x10110)
x11010 .prod(x10, x11000)
x100010 .prod(x1100, x10110)
x110101 .prod(x10011, x100010)
x111011 .prod(x110, x110101)
x1001011 .prod(x10110, x110101)
x1001101 .prod(x10, x1001011)
x1010101 .prod(x11010, x111011)
x1100111 .prod(x10010, x1010101)
x1101001 .prod(x10, x1100111)
x10000011 .prod(x11010, x1101001)
x10011001 .prod(x10110, x10000011)
x10011101 .prod(x100, x10011001)
x10111111 .prod(x100010, x10011101)
x11010111 .prod(x11000, x10111111)
x11011011 .prod(x100, x11010111)
x11100111 .prod(x1100, x11011011)
x11101111 .prod(x11000, x11010111)
x11111111 .prod(x11000, x11100111)
# 26 operations

let a = a # Allow aliasing between r and a

# 26+28 = 54 operations
r.square_repeated(x11100111, 8)
r *= x11011011
r.square_repeated(9)
r *= x10011101
r.square_repeated(9)

# 54 + 20 = 74 operations
r *= x10011001
r.square_repeated(9)
r *= x10011001
r.square_repeated(8)
r *= x11010111

# 74 + 27 = 101 operations
r.square_repeated(6)
r *= x110101
r.square_repeated(10)
r *= x10000011
r.square_repeated(9)

# 101 + 19 = 120 operations
r *= x1100111
r.square_repeated(8)
r *= x111011
r.square_repeated(8)
r *= a

# 120 + 41 = 160 operations
r.square_repeated(14)
r *= x1001101
r.square_repeated(10)
r *= x111011
r.square_repeated(15)

# 161 + 21 = 182 operations
r *= x1010101
r.square_repeated(10)
r *= x11101111
r.square_repeated(8)
r *= x1101001

# 182 + 33 = 215 operations
r.square_repeated(16)
r *= x10111111
r.square_repeated(8)
r *= x11111111
r.square_repeated(7)

# 215 + 20 = 235 operations
r *= x1001011
r.square_repeated(9)
r *= x11111111
r.square_repeated(8)
r *= x10111111

# 235 + 26 = 261 operations
r.square_repeated(8)
r *= x11111111
r.square_repeated(8)
r *= x11111111
r.square_repeated(8)

# 261 + 3 = 264 operations
r *= x11111111
r.square()
r *= a
2 changes: 1 addition & 1 deletion constantine/math/constants/zoo_square_roots.nim
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Expand Up @@ -47,7 +47,7 @@ macro tonelliShanks*(C: static Curve, value: untyped): untyped =
return bindSym($C & "_TonelliShanks_" & $value)

func hasTonelliShanksAddchain*(C: static Curve): static bool =
when C in {BLS12_377}:
when C in {Bandersnatch, Banderwagon, BLS12_377}:
true
else:
false
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