Shamira Changeset - db65075fe7e0

Changeset - db65075fe7e0

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Laman - 8 years ago 2017-09-17 22:36:32

reconstructing the secret

2 files changed with 21 insertions and 1 deletions:

src/gf256.py

src/shamira.py

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src/gf256.py

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 def _ffmul(a, b):
 	r=0
 	while a!=0:
 		if (a&1)!=0: r^=b
 		t=b&0x80
 		b=(b<<1)&255
 		if t!=0: b^=0x1b
 		a>>=1
 	return r
 g=3
 E=[None]*256
 L=[None]*256
 acc=1
 for i in range(256):
 	E[i]=acc
 	L[acc]=i
 	acc=_ffmul(acc, g)
 L[1]=0
 inv=[E[255-L[i]] if i!=0 else None for i in range(256)]
 def ffmul(a, b):
 	if a==0 or b==0: return 0
 	t=L[a]+L[b]
 	if t>255: t-=255
 	return E[t]
 def evaluate(coefs,x):
 	res=0
 	xK=1
 	for a in coefs:
 		res^=ffmul(a,xK)
 		xK=ffmul(xK,x)
 	return res
 def getConstantCoef(k,*points):
 	res=0
 	for i in range(k):
 		(x,y)=points[i]
 		prod=1
 		for j in range(k):
 			if i==j: continue
 			(xj,yj)=points[j]
 			prod=ffmul(prod, (ffmul(xj,inv[xj^x])))
 		res^=ffmul(y,prod)
 	return res

src/shamira.py

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 import os
 import gf256
 def shareByte(secretB,k,n):
 	assert n<255
 	coefs=[int(secretB)]+[int(b) for b in os.urandom(k-1)]
 	points=[gf256.evaluate(coefs,i) for i in range(1,n+1)]
 	return points
 def generate(secret,k,n):
 	shares=[shareByte(b,k,n) for b in secret]
 	return [(i+1, [s[i] for s in shares]) for i in range(n)]
 print(generate(b"key",2,3))
 def reconstruct(*shares):
 	k=len(shares)
 	secretLen=len(shares[0][1])
 	res=[None]*secretLen
 	for i in range(secretLen):
 		bs=[(x,s[i]) for (x,s) in shares]
 		res[i]=(gf256.getConstantCoef(k,*bs))
 	return bytes(res)

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