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Added krzywa.rb and module

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Signed-off-by: Marcin Woźniak <y0rune@aol.com>
This commit is contained in:
Marcin Woźniak 2020-12-12 01:14:07 +01:00
parent 37b5b68451
commit dcd6ab195d
Signed by: y0rune
GPG Key ID: F204C385F57EB348
2 changed files with 66 additions and 18 deletions
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77
6/krzywa.rb
View File

@ -24,7 +24,7 @@ def delta(a,b,p)
end
def rownanieKrzywej(a,b,p,x)
fx = (betterExponentiation(x,3,p) + (a * x) % p + b % p) % p
fx = ((betterExponentiation(x,3,p) + (a * x) % p + b % p) % p) % p
return fx
end
@ -55,23 +55,19 @@ def generatorKrzywej(p)
end
def punktNaKrzywej(a,b,p)
if delta(a,b,p) != 0
while true
x = SecureRandom.random_number(1..p-1)
if delta(a,b,p) != 0
while true
x = SecureRandom.random_number(1..p-1)
fx = rownanieKrzywej(a,b,p,x)
if remSqEuler(fx,p)
if a == 0
y = 0
elsif p == 2
y = p
elsif p % 4 == 3
y = Math.sqrt(fx).to_i % p
#y = betterExponentiation(a,(p+1/4),p)
if p % 4 == 3
#y = Math.sqrt(fx).to_i % p
y = betterExponentiation(x,(p+1/4),p)
end
return x,y
end
end
end
end
end
end
def czyPunktNalezyDoKrzywej(a,b,p,x,y)
@ -80,6 +76,7 @@ def czyPunktNalezyDoKrzywej(a,b,p,x,y)
if fx == betterExponentiation(y,2,p)
return true
else
puts rownanieKrzywej(a,b,p,x).inspect
return false
end
end
@ -98,12 +95,13 @@ def sumaPunktow(a,b,p,x1,y1,x2,y2)
end
# P + -Q = 0 DZIALA
if (x1 == x2) && (y1 == -y2)
puts "0 - el.neutralny"
return "0"
end
# P + P = 2P DZIALA
if (x1 == x2) && (y1 == y2)
alpha = (((3 * betterExponentiation(x1,2,p) % p + a) % p) * reciprocal_Phi_p(2 * y1,p)) % p
x3 = betterExponentiation(alpha,2,p) - (x1 % p) - (x2 % p)
x3 = (betterExponentiation(alpha,2,p) - (x1 % p) - (x2 % p)) % p
y3 = (alpha * (x1 - x3) - y1) % p
return x3,y3
end
@ -112,8 +110,7 @@ def sumaPunktow(a,b,p,x1,y1,x2,y2)
return x2,y2
elsif (x2 == 0 && y2 == 0)
return x1,y1
end
end
end
#puts generatorKrzywej(11).inspect
@ -164,3 +161,51 @@ puts sumaPunktow(a,b,p,xp,yp,xq,yq).inspect
# 4) 2R
puts sumaPunktow(a,b,p,xp,yp,xp,yp).inspect
##################################################
#puts generatorKrzywej(1183779584357076950937981497685946292711107412152534481102525547387604378262522402526266939).inspect
#puts punktNaKrzywej(239614427021073265587611886177902927263167863041565491257781227550405368115731464059190159,447169285435982716467332439542997876345372330045685811964291613238129105735899852114277221,1183779584357076950937981497685946292711107412152534481102525547387604378262522402526266939).inspect
#puts czyPunktNalezyDoKrzywej(2,7,11,7,1).inspect
#puts czyPunktNalezyDoKrzywej(2,7,11,2,2).inspect
#puts punktPrzeciwny(2,2).inspect
#puts sumaPunktow(2,2,17,5,1,5,1).inspect
# Zadanie od profersora
a=239614427021073265587611886177902927263167863041565491257781227550405368115731464059190159
b=447169285435982716467332439542997876345372330045685811964291613238129105735899852114277221
p=1183779584357076950937981497685946292711107412152534481102525547387604378262522402526266939
px=285113634279465403319996581740169338329454608669814309137990174814243655992779447106132850
py=598700530906084162596261101440667782569915319623798143751082061599951188013331503150304328
# Zadanie 1
puts
puts "Zadanie 1"
puts generatorKrzywej(p).inspect
# Zadanie 2
puts
puts "Zadanie 2"
puts punktNaKrzywej(a,b,p).inspect
# Zadanie 3
puts
puts "Zadanie 3"
puts czyPunktNalezyDoKrzywej(a,b,p,px,py).inspect
# Zadanie 4
puts
puts "Zadanie 4"
puts punktPrzeciwny(px,py).inspect
# Zadanie 5
puts
puts "Zadanie 5"
q=sumaPunktow(a,b,p,px,py,px,py).inspect
puts "P+P=Q=" + q.inspect
qx=q[0].to_i
qy=q[1].to_i
r=sumaPunktow(a,b,p,px,py,qx,qy).inspect
puts "P+Q=R=" + r.inspect

7
module.rb
View File

@ -114,6 +114,10 @@ def betterExponentiation(x,k,n)
return false
end
if x == 0
return 0
end
if x < n && x > 0
b = k.to_s(2).reverse
l = b.count "[0-1]"
@ -140,8 +144,7 @@ end
####################################
def remSqEuler(a,p)
ans = betterExponentiation(a,(p-1)/2,p)
if ans == 1 && Prime.prime?(p)
if ans == 1 && primalityTest(p)
return true
else
return false