160 lines
3.2 KiB
Ruby
Executable File
160 lines
3.2 KiB
Ruby
Executable File
#!/usr/bin/ruby
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# coding: utf-8
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#######################################
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#
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# Marcin Woźniak
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# s434812
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#
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########################################
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load '../module.rb'
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require 'thread'
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require 'thwait'
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def returnRownanie(a,b,p)
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puts
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puts "Równanie krzywej jest równe: " + "Y^2 = X^3+" + a.inspect + "X+" + b.inspect + " mod "+ p.inspect
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puts
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end
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def delta(a,b,p)
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d = ((4 * betterExponentiation(a,3,p) % p) + (27 * betterExponentiation(b,2,p) % p)) % p
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return d
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end
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def rownanieKrzywej(a,b,p,x)
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fx = (betterExponentiation(x,3,p) + (a * x) % p + b % p) % p
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return fx
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end
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def generatorKrzywej(p)
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a = 0
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b = 0
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while true
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if primalityTest(p) && p % 4 == 3
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threads = []
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threads << Thread.new {
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a = SecureRandom.random_number(1..p-1)
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}
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threads << Thread.new {
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b = SecureRandom.random_number(1..p-1)
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}
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ThreadsWait.all_waits(*threads)
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if delta(a,b,p) != 0
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returnRownanie(a,b,p)
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return a,b
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end
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end
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end
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end
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def punktNaKrzywej(a,b,p)
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if delta(a,b,p) != 0
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while true
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x = SecureRandom.random_number(1..p-1)
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fx = rownanieKrzywej(a,b,p,x)
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if remSqEuler(fx,p)
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if a == 0
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y = 0
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elsif p == 2
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y = p
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elsif p % 4 == 3
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y = Math.sqrt(fx).to_i % p
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#y = betterExponentiation(a,(p+1/4),p)
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end
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return x,y
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end
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end
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end
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end
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def czyPunktNalezyDoKrzywej(a,b,p,x,y)
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fx = rownanieKrzywej(a,b,p,x)
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if fx == betterExponentiation(y,2,p)
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return true
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else
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return false
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end
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end
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def punktPrzeciwny(x,y)
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return x,-y
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end
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def sumaPunktow(a,b,p,x1,y1,x2,y2)
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# P + Q = R
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if (x1 != x2) && (y1 != y2)
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alpha = (((y2 - y1) % p) * reciprocal_Phi_p((x2 - x1),p)) % p
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x3 = (betterExponentiation(alpha,2,p) - (x1 % p) - (x2 % p)) % p
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y3 = (alpha * (x1 - x3) - y1) % p
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return x3,y3
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end
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# P + -Q = 0 DZIALA
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if (x1 == x2) && (y1 == -y2)
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return "0"
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end
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# P + P = 2P DZIALA
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if (x1 == x2) && (y1 == y2)
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alpha = (((3 * betterExponentiation(x1,2,p) % p + a) % p) * reciprocal_Phi_p(2 * y1,p)) % p
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x3 = betterExponentiation(alpha,2,p) - (x1 % p) - (x2 % p)
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y3 = (alpha * (x1 - x3) - y1) % p
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return x3,y3
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end
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# 0 - element neutrany --> P + 0 = P
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if (x1 == 0 && y1 == 0 )
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return x2,y2
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elsif (x2 == 0 && y2 == 0)
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return x1,y1
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end
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end
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#puts generatorKrzywej(11).inspect
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#puts punktNaKrzywej(2,7,11).inspect
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#puts czyPunktNalezyDoKrzywej(2,7,11,7,1).inspect
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#puts czyPunktNalezyDoKrzywej(2,7,11,2,2).inspect
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#puts punktPrzeciwny(2,2).inspect
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#puts sumaPunktow(2,2,17,5,1,5,1).inspect
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##################################################
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# Zadania z konca wykladu suma punktow
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#
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# Niech E/F7 będzie postaci
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# E : Y^2 = X^3 + 1
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#
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# Niech P=(1,3) Q=(2,4) R=(6,0)
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#
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# Obliczyc:
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# 1) -Q
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# 2) R + [0,0]
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# 3) P + Q
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# 4) 2R
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#
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##################################################
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# Rozwiązanie:
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a = 0
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b = 1
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p = 7
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xp = 1
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yp = 3
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xq = 2
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yq = 4
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xr = 6
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yr = 0
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puts punktPrzeciwny(xq,yq).inspect
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puts sumaPunktow(a,b,p,xr,yr,0,0).inspect
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puts sumaPunktow(a,b,p,xp,yp,xq,yq).inspect
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puts sumaPunktow(a,b,p,xp,yp,xp,yp).inspect
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##################################################
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