def Gen_response(self,slist,split_ID,hksplit_ID):#t代表多项式的项数，n代表分片的数量
pairing = global_variable.get_pairing()
g1 = global_variable.get_g1()
self.__response = gmpy2.mpz(0)
coef_hk = dict()
for i in range(len(slist)-2):
temp = slist[i]
temp1 = hksplit_ID[len(slist)-1-i]
temp2 = gmpy2.mul(temp , temp1)
temp2 = gmpy2.f_mod(temp2,q)
coef_hk[i+2] = temp2
#存m个f(i)+a[i]连乘的结果
fk_ID = (np.polyval(slist,split_ID))
fk_ID = fk_ID % q
for l in coef_hk:
coefhk = coef_hk[l]
fk_ID = gmpy2.sub(fk_ID , coefhk)
fk_ID = fk_ID % q
self.__response = fk_ID
self.__comm_response_ID = Element(pairing, G1)
self.__comm_response_ID = g1 ** int(self.__response)
return self.__comm_response_ID,self.__response
def __Gen_vk(self, t, n, k):
#获取全局变量
pairing = global_variable.get_pairing()
g1 = global_variable.get_g1()
#生成秘密 secret 的承诺
secret_k = dict()
secret = self.__f[0]
temp = secret
secret_k[1] = secret
for i in range(k):
if i >= 1:
temp = gmpy2.mul(temp, secret)
temp = gmpy2.f_mod(temp, q)
secret_k[i + 1] = temp
commitment_s_i = Element(pairing, G1)
self.__commitment_s = dict()
for i in secret_k:
commitment_s_i = g1**int(secret_k[i])
self.__commitment_s[i] = commitment_s_i
#print ("commitment_s = \n",self.__commitment_s)
#生成 f(x) 的承诺
commitment_fx_coef = self.__comm(self.__f, 1, t, pairing, g1)
print("the commitment of fx = \n", commitment_fx_coef)
self.__commitment_fx_joint = str(commitment_fx_coef[0])
for i in range(t - 1):
self.__commitment_fx_joint = self.__commitment_fx_joint + str(
commitment_fx_coef[i + 1])
#print("the joint of fx = \n",self.__commitment_fx_joint)
#生成 r
self.__r = 0
r = sha256()
r.update(self.__commitment_fx_joint.encode("utf8"))
dr = r.hexdigest()
self.__r = int(dr, 16)
self.__r = gmpy2.mpz(self.__r)
self.__r = gmpy2.f_mod(self.__r, q)
#print("r = \n",self.__r)
#生成 f(r) 和 f(r)^k 的承诺
self.__commitment_fr_k = dict()
fr = self.__fun(self.__f, 1, t, self.__r)
comm_fr = Element(pairing, G1)
comm_fr = g1**int(fr)
self.__commitment_fr_k[1] = comm_fr
fr_i = fr
for i in range(k - 1):
fr_i = fr_i * fr
comm_fr_i = Element(pairing, G1)
comm_fr_i = g1**int(fr_i)
self.__commitment_fr_k[i + 2] = comm_fr_i
print("commitment_fr_k = \n", self.__commitment_fr_k)
#生成 ck(x) 的承诺
commitment_ck_coef = dict()
self.__commitment_ck_joint = dict()
for i in self.__ck:
commitment_ck_i = list()
ck_i = self.__ck[i]
commitment_ck_i = self.__comm(ck_i, 1, t, pairing, g1)
commitment_ck_coef[i] = commitment_ck_i
#print("commitment_ck_coef = \n", commitment_ck_coef)
for i in commitment_ck_coef:
comm_ci_coef = commitment_ck_coef[i]
str_comm_ci_coef = str(comm_ci_coef[0])
str_comm_ci_coef = str_comm_ci_coef[:130]
for j in range(t - 1):
str_comm_ci_coef = str_comm_ci_coef + str(comm_ci_coef[j + 1])
self.__commitment_ck_joint[i] = str_comm_ci_coef
#print("commitment_ck_joint = \n",self.__commitment_ck_joint)
#生成 hk(x) 的承诺
commitment_hk_coef = dict() #用于存储基点与hk各个系数的点乘结果
self.__commitment_hk_joint = dict() #用于存储拼接后的hk的承诺
for i in self.__hk:
commitment_hk_i = list()
hk_i = self.__hk[i]
commitment_hk_i = self.__comm(hk_i, i, t, pairing, g1)
commitment_hk_coef[i] = commitment_hk_i
#print("commitment_hk_coef = \n",commitment_hk_coef)
for i in commitment_hk_coef:
comm_hi_coef = commitment_hk_coef[i]
str_comm_hi_coef = str(comm_hi_coef[0])
str_comm_hi_coef = str_comm_hi_coef[:130]
for j in range(i * t - i):
str_comm_hi_coef = str_comm_hi_coef + str(comm_hi_coef[j + 1])
self.__commitment_hk_joint[i] = str_comm_hi_coef
#print("commitment_hk_joint = \n",self.__commitment_hk_joint)
#生成 f(x) 分片 f(i) 的承诺,用于安全传输
self.__commitment_split = dict()
for i in self.__split:
comm_split = Element(pairing, G1)
comm_split = g1**int(self.__split[i])
self.__commitment_split[i] = comm_split
#print("commitment_split = \n",self.__commitment_split)
#生成 hk(x) 分片 hk(i) 的承诺,用于安全传输
self.__commitment_hk_split = dict()
for i in self.__hksplit:
hksplit_key = self.__hksplit[i]
comm_hksplit_key = dict()
for key in hksplit_key:
comm_hksplit = Element(pairing, G1)
comm_hksplit = g1**int(hksplit_key[key])
comm_hksplit_key[key] = comm_hksplit
self.__commitment_hk_split[i] = comm_hksplit_key
def __verify_com(self,k,t,commitment_s,commitment_fx_joint,commitment_fr_k,commitment_ck_joint,commitment_hk_joint):
#获取全局变量
pairing = global_variable.get_pairing()
g1 = global_variable.get_g1()
#用来记录验证成功的次数
success_num = 0
#验证秘密 secret 的承诺
count = 0
temp1 = Element(pairing, G1)
temp2 = Element(pairing, G1)
for i in range(k):
if i >= 1:
temp1 = pairing.apply(commitment_s[1], commitment_s[i])
temp2 = pairing.apply(commitment_s[i+1], g1)
if (temp1 == temp2):
count = count + 1
print("the verify for commitment of secret is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^")
else:
print("the verify for commitment of secret is:>~< >~< >~< >~< >~< >~<fail!>~< >~< >~< >~< >~< >~<")
if count == k-1:
success_num = success_num + 1
#生成 r'
r = 0
rt = sha256()
rt.update(commitment_fx_joint.encode("utf8"))
dr = rt.hexdigest()
r = int(dr,16)
r = gmpy2.mpz(r)
r = gmpy2.f_mod(r,q)
print("r' = \n",r)
#处理以字符串形式拼接起来的承诺 CM_fx,并生成CM_fr'
temp = commitment_fx_joint
str_fx = re.findall(r'.{130}', temp)
#print("str_fx = \n",str_fx)
gfr_list = list()
for i in range(len(str_fx)):
temp = Element(pairing,G1,value = str_fx[i])
ri = gmpy2.powmod(r,i,q)
temp = temp ** int(ri)
gfr_list.append(temp)
#print("gfr_list = \n",gfr_list)
gfr = Element(pairing,G1)
for i in range(len(gfr_list)):
gfr = gfr * gfr_list[i]
#验证秘密 fk(r) 的承诺
count = 0
temp3 = Element(pairing, G1)
temp4 = Element(pairing, G1)
for j in range(k):
if j >= 1:
temp3 = pairing.apply(gfr, commitment_fr_k[j])
temp4 = pairing.apply(commitment_fr_k[j+1], g1)
if (temp3 == temp4):
count = count + 1
print("the verify for commitment of fk(r) is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^")
else:
print("the verify for commitment of fk(r) is:>~< >~< >~< >~< >~< >~<fail!>~< >~< >~< >~< >~< >~<")
if count == k-1:
success_num = success_num + 1
#处理以字符串形式拼接起来的承诺 CM_ck
com_ck = dict()
for key in commitment_ck_joint:
com_cki = list()
temp = commitment_ck_joint[key]
str_ck = re.findall(r'.{130}', temp)
#print("str_ck = \n",str_ck)
for i in range(len(str_ck)):
temp1 = Element(pairing,G1,value = str_ck[i])
com_cki.append(temp1)
com_ck[key] = com_cki
#print("com_ck = \n",com_ck)
#生成 ck(r') 的承诺
commitment_ck_r = dict()
temp1 = list()
for key in com_ck:
comm_ck_r = list()
temp1 = com_ck[key]
temp2 = Element(pairing,G1)
for i in range(t):
temp2 = temp1[i] ** int(r ** i)
comm_ck_r.append(temp2)
temp3 = Element(pairing,G1)
temp3 = comm_ck_r[0]
for j in range(t-1):
temp3 = temp3 * comm_ck_r[j+1]
commitment_ck_r[key] = temp3
#print("commitment_ck_r = \n",commitment_ck_r)
#生成 hk(r') 的承诺
com_hk = dict()
for key in commitment_hk_joint:
com_hki = list()
temp = commitment_hk_joint[key]
str_hk = re.findall(r'.{130}', temp)
for i in range(len(str_hk)):
temp1 = Element(pairing,G1,value = str_hk[i])
com_hki.append(temp1)
com_hk[key] = com_hki
#print("com_hk = \n",com_hk)
temp1 = Element(pairing, G1)
commitment_hk_r = dict()
for key in com_hk:
temp3 = list()
temp2 = com_hk[key]
for j in range(key*t-key+1):
temp1 = temp2[j]**int(r**j)
temp3.append(temp1)
temp4 = Element(pairing, G1)
temp4 = temp3[0]
for k in range(key*t-key):
temp4 = temp4 * temp3[k+1]
commitment_hk_r[key] = temp4
#print("commitment_hk_r = \n",commitment_hk_r)
commitment_hk_r1 = dict()
temp = Element(pairing, G1)
for i in commitment_ck_r:
temp = commitment_fr_k[i]-commitment_ck_r[i]-commitment_s[i]
commitment_hk_r1[i] = temp
#print ("commitment_hk_r1 = \n",commitment_hk_r1)
#验证秘密 hk(r) 的承诺
count = 0
for key in commitment_hk_r1:
if commitment_hk_r1[key] == commitment_hk_r[key]:
count = count + 1
print("the verify for commitment of hk(r) is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^")
else:
print("the verify for commitment of hk(r) is:>~< >~< >~< >~< >~< >~<fail!>~< >~< >~< >~< >~< >~<")
if count == len(commitment_hk_r1):
success_num = success_num + 1
#汇总验证结果
if success_num == 3:
return True
def __verify_core_share(self,k,t,commitment_split,commitment_hk_split,commitment_fx_joint,commitment_hk_joint,ID):
#获取全局变量
pairing = global_variable.get_pairing()
#用来记录验证成功的次数
success_num = 0
#验证分片 fi 的承诺
count = 0
com_fx_coef = list()
temp = commitment_fx_joint
str_fx = re.findall(r'.{130}', temp)
for i in range(len(str_fx)):
temp = Element(pairing,G1,value = str_fx[i])
com_fx_coef.append(temp)
#print("com_fx_coef = \n",com_fx_coef)
commitment_fID = Element(pairing, G1)
comm_fi = Element(pairing, G1)
temp2 = Element(pairing, G1)
commitment_fxcoef_ID = list()
for j in range(t):
temp2 = com_fx_coef[j] ** int(ID**j)
commitment_fxcoef_ID.append(temp2)
#print("commitment_fxcoef_ID = ",commitment_fxcoef_ID)
comm_fi = commitment_fxcoef_ID[0]
for m in range(t-1):
comm_fi = comm_fi * commitment_fxcoef_ID[m+1]
commitment_fID = comm_fi
#print("commitment_fID = ",commitment_fID)
if commitment_fID == commitment_split[ID]:
count = count + 1
print("the verify for commitment of fi is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^")
else:
print("the verify for commitment of fi is:>~< >~< >~< >~< >~< >~<fail!>~< >~< >~< >~< >~< >~<")
if count == len(commitment_fID):
success_num = success_num + 1
#验证分片 hki 的承诺
count = 0
temp1 = Element(pairing, G1)
temp4 = Element(pairing, G1)
commitment_hk_i = dict()
com_hk = dict()
for key in commitment_hk_joint:
com_hki = list()
temp = commitment_hk_joint[key]
str_hk = re.findall(r'.{130}', temp)
for i in range(len(str_hk)):
temp1 = Element(pairing,G1,value = str_hk[i])
com_hki.append(temp1)
com_hk[key] = com_hki
#print("com_hk = ",com_hk)
for key in com_hk:
com_hk_key = com_hk[key]
comm_hk_ii = list()
for j in range(key*t-key+1):
temp1 = com_hk_key[j]**int(ID**j)
comm_hk_ii.append(temp1)
temp4 = comm_hk_ii[0]
for k in range(key*t-key):
temp4 = temp4 * comm_hk_ii[k+1]
commitment_hk_i[key] = temp4
print("commitment_hk_i = ",commitment_hk_i)
if commitment_hk_split[ID] == commitment_hk_i:
count = count + 1
print("the verify for commitment of hksplit is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^")
else:
print("the verify for commitment of hksplit is:>~< >~< >~< >~< >~< >~<fail!>~< >~< >~< >~< >~< >~<")
if count == len(commitment_hk_split):
success_num = success_num + 1
if success_num == 2:
return True
def verify_response_comm(self, slist, t, ID, commitment_fx_joint,
commitment_s, commitment_cx_joint,
comm_response_ID):
pairing = global_variable.get_pairing()
g1 = global_variable.get_g1()
self.__response_coef_comm = dict()
commitment_cx = dict() # 存储ck(ID)的承诺
commitment_fx = dict() # 存储f(ID)^k的承诺
com_ck = dict() # 存ck(x)系数的承诺
for key in commitment_cx_joint:
if key <= (len(slist) - 1):
com_cki = list() # 中间变量
temp = commitment_cx_joint[key]
str_ck = re.findall(r'.{130}', temp)
for i in range(len(str_ck)):
temp1 = Element(pairing, G1, value=str_ck[i])
com_cki.append(temp1)
com_ck[key] = com_cki
com_ck_key = com_ck[key]
comm_ck_coef_i = list()
for j in range(t):
temp2 = com_ck_key[j]**(int(ID)**j)
comm_ck_coef_i.append(temp2)
temp3 = comm_ck_coef_i[0]
for j in range(t - 1):
temp3 = temp3 * comm_ck_coef_i[j + 1]
commitment_cx[key] = temp3
temp = commitment_fx_joint
str_fx = re.findall(r'.{130}', temp)
gfr_list = list()
for i in range(len(str_fx)):
temp1 = Element(pairing, G1, value=str_fx[i])
gfr_list.append(temp1)
comm_fk_coef_i = list()
for j in range(t):
temp2 = gfr_list[j]**(int(ID)**j)
comm_fk_coef_i.append(temp2)
temp3 = comm_fk_coef_i[0]
for j in range(t - 1):
temp3 = temp3 * comm_fk_coef_i[j + 1]
commitment_fx = temp3
commck_mul_commsk = dict() # 存储ck(ID)的承诺*s^k的承诺
for key in commitment_cx:
temp1 = commitment_cx[key] * commitment_s[key]
commck_mul_commsk[key] = temp1
if (len(slist) - 1) > 1:
response_commcksk = dict()
for i in range(len(slist) - 1):
if i + 2 <= len(slist) - 1:
temp1 = commck_mul_commsk[i + 2]
temp = temp1**int(slist[len(slist) - i - 3])
response_commcksk[i + 2] = temp
temp2 = response_commcksk[2]
for i in response_commcksk:
if i != 2:
temp3 = response_commcksk[i]
temp2 = temp2 * temp3
self.__response_coef_comm = temp2 * \
(commitment_fx**int(slist[len(slist)-2])
)*(g1**int(slist[len(slist)-1]))
else:
self.__response_coef_comm = (commitment_fx**int(
slist[len(slist) - 2])) * (g1**int(slist[len(slist) - 1]))
#print("response_coef_comm = ",self.__response_coef_comm)
if comm_response_ID == self.__response_coef_comm:
print(
"the verify for response is:^-^ ^-^ ^-^ ^-^ ^-^ ^-^success!^-^ ^-^ ^-^ ^-^ ^-^ ^-^"
)
else:
print(
"the verify for response is:>~< >~< >~< >~< >~< >~<fali!>~< >~< >~< >~< >~< >~<"
)