#d = 112355821013181156334579806714681205113924101983091861382414581448074528853593605127763129459607001465442516908138238424303909864293999123027639058680152442574950795353128551552720849511889171655164974758120631156315783552861760016539440473035738314285696233932793785419140238228427811142518736338748655534216
#d = 133857774395556098823468076626040347428204866818519542402902008784242273588316831913605996105230853461276135011422723944412845259711225048858837394986306394647391907198726511192712952714328510682163669967335973252036472304294328739156120877752865219694442283089125533996403824366372974853733187988425356295024
#d = 92672982967554862852872006766567885353927794137150728379364376690926427171759450260823444154424352669428620565618041049755868480284199412293078394066055239894180641830867546527203202271291597555024007333879865905283486866630899589672475264171999801451395902946562129189391119900984175066161729889310646122594
#d = 113813244351128015985725472713799074858302071177559053942112014638788671381991253282405181172424524305518788455655662991697764200854729806319332367596212279599001943195420594782844193398223385020569219824365726550599798813591088325549820289065752592119059411046289242404680945642950558285906917488427350067624
#d = 154306836123321631119810799993069910562141298931598323240160602873671313236111868972030294077912144521304411731326072185184552318703310573606495608896444935154732549995879559329450180425460887277250996580725663464080385147621501500334111997031535773362131377142103450071529478728786081711354141515585781890867
#d = 144158195593448605833804358266959731071319524602506883655484058320858197715337147221541236215995256052433774784893470051901675638209433372179900041158152554361983763960343665324874540181999367855835609860134390778783899662849805853369844243552402213219357445415050466245170450596556905770235758017088277438463
#d = 133882584169402263649273269380196608150084375269146243075496885327405606895985408568168074590228694708438736519641709599822579193115157935449659948346845017681175549217934255050505731490489216233723387151881486768711240179550970803743221393089463044661701791371054424648342246977177087977856380921510782107615
#d = 89890143019078095666205291519192456199494286740069204913245222910175469067352905557250874673542291519764568367690661504881757821856674244313802393186064887816981967011575839272828011803696604070384573895899003090207346702274748477045360023825244474240081997951823651945005117885273906197385377692060280309872
#d = 179769313486231550846377820112651619934450204046286207089508497640609636080136379993475607411279856471548734596191771850457170532144305191108817379111947852937804676159408642833589618669094281927243886543216063460892657915213572256793106748888238068024466511814056459351928721043252931840952970109551898525693
#d = 138077524384358897387044254528942666865362436963425081806222678029623527212561397169625919256841085997842460692685629820335432379563877502861077662100645851747408164039505064751503719854570729630741324273793686789643069754389888125919913610491927011554612571257339014291317914843276351034098443218764569772032
#d = 112399902876706645855193200215846797377686746602348093309395081305273711708872277912471569972950225871079503530829845264090289742903812768541381031778883678678641113130026814629247250025509579187903678182812889146989970235966832273151062245438395886319290591445432792632323908362447250818793593858283557355522
#d = 102292777480667301538680215936936970283092621829031321200241989331682699365974716872354801193947415645909294390183956243605147184376659696804092413123017374096080271856608472255086366623878981317181944936395399158744668440601249710010755921860415444235147513673664907034438157378610303883773088414762812422029
d = 179769313486230293476729321456568711106334152553137915895549523442135975529688892045243765355877820600277606527886009475314273959881378474590711686871215518410475081291639017048244081934993792064218187859314222021261959843396508002327741826742350432873271262317803816765741246938839638072935076868657199972351
print('\n\n************* {0}回目 ***************'.format(i + 1))
print('******** c = {0} , d = {1}, {2} ********\n'.format(
c, bin.binary_d(d), d))
#print('******** c = {0} , d = {1}, {2} , e = {3} ********\n'.format(c, bin.binary_d(d), d, e))
# 以下, バイナリ法の実施により,
# 平文mとカウント数countを計算
print('*************binary_method*************')
m1, mod_count1, mult_count1 = bin.binary_method(c, d, N)
binary_mod_count_list.append(mod_count1)
binary_mult_count_list.append(mult_count1)
binary_sum_count_list.append(mod_count1 + mult_count1)
bin.average(binary_mod_count_list)
bin.average(binary_mult_count_list)
bin.average(binary_sum_count_list)
#print('c = {0}, d = {1}, N = {2}'.format(c, d, N))
print('binary(c, d, N) = {0}'.format(m1))
print('mod_count = {0}'.format(mod_count1))
def crt(c, d, N, p, q):
mod_count = 0
mult_count = 0
#
# あらかじめ計算しておく部分
#
d_p = d % (p - 1)
d_q = d % (q - 1)
#d_p, _ = bin.modulo(d, p-1, mod_count)
#d_q, _ = bin.modulo(d, q-1, mod_count)
q_dash = mod_equal_1_crt(q, p)
#print('q_dash = {0}'.format(q_dash))
"""
# Q, Pの計算
# countの操作はしなくて良い.
# あらかじめ計算しなければいけないものなので.
y = mod_equal_1_crt(q, p)
x = mod_equal_1_crt(p, q)
# 以下の二つはcountを操作しなくて良い
# あらかじめ計算しなければいけないものなので.
Q, _ = bin.modulo(q*y, N, 0)
P, _ = bin.modulo(p*x, N, 0)
"""
#
# 以上, あらかじめ計算しておく部分
#
"""
#print('\n\nc={0}, d={1}, N={2}, p={3}, q={4}'.format(c,d,N,p,q))
print('================= CRT(c:{0}, d:{1}, N:{2}, p:{3}, q:{4}) ================='.format(c, d, N, p, q))
a, mod_count1, mult_count1 = mon.mod_bin(c, d, p)
print('c**d mod p = {0}'.format(a))
b, mod_count2, mult_count2 = mon.mod_bin(c, d, q)
print('c**d mod q = {0}'.format(b))
#print('\na = {0}, b = {1}'.format(a, b))
mod_count = mod_count1 + mod_count2
mult_count = mult_count1 + mult_count2
aq, mult_count = bin.multiply(a, Q, mult_count)
bp, mult_count = bin.multiply(b, P, mult_count)
aqbp = aq + bp
ans, mod_count = bin.modulo(aqbp, N, mod_count)
"""
#print('================= CRT(c:{0}, d:{1}, N:{2}, p:{3}, q:{4}) ================='.format(c, d, N, p, q))
#c_p = c % p
c_p, mod_count = bin.modulo(c, p, mod_count)
#print('c_p = c % p = {0} % {1} = {2}'.format(c, p, c_p))
print('d_p = d % (p-1) = {0} % {1} = {2}'.format(d, p - 1, d_p))
print('d_pの2進数表現 = {0}'.format(bin.binary_d(d_p)))
#c_q = c % q
c_q, mod_count = bin.modulo(c, q, mod_count)
#print('c_q = c % q = {0} % {1} = {2}'.format(c, q, c_q))
print('d_q = d % (q-1) = {0} % {1} = {2}'.format(d, q - 1, d_q))
print('d_qの2進数表現 = {0}'.format(bin.binary_d(d_q)))
m_p, mod_count1, mult_count1, _, _, _, _ = mon.mod_bin(c_p, d_p, p)
#print('(c_p)**(d_p) mod p = {0}'.format(m_p))
m_q, mod_count2, mult_count2, _, _, _, _ = mon.mod_bin(c_q, d_q, q)
#print('(c_q)**(d_q) mod q = {0}'.format(m_q))
mod_count += (mod_count1 + mod_count2)
mult_count += (mult_count1 + mult_count2)
x, mult_count = bin.multiply(q_dash, (m_p - m_q), mult_count)
y, mod_count = bin.modulo(x, p, mod_count)
z, mult_count = bin.multiply(y, q, mult_count)
ans = m_q + z
#ans = m_q + (q_dash * (m_p - m_q) mod p)
return ans, mod_count, mult_count
def mod_bin(c, d, N):
global countMM
global countMC
global countNG_MM
global countNG_MC
global MM_list
global MC_list
countMM = 0
countMC = 0
countNG_MM = 0
countNG_MC = 0
array_N = bin.binary_d(N)
#print('\n\narray_N = {0}'.format(array_N))
length_N = len(array_N)
#print('length_N = {0}'.format(length_N))
R = 2**length_N
R_2 = R * R % N
N_dash = mod_equal_minus_1(N, R)
mod_count = 0
mult_count = 0
#print('c = {0}, d = {1}, N = {2}'.format(c, d, N))
#print('c={0}, d={1}, N={2}, R={3}, R_2={4}, N_dash={5}'.format(c,d,N,R,R_2,N_dash))
"""
質問その4：RとR_2の計算はカウント対象でない (ついでにRの計算方法があっているかを確認する).
"""
#print('length_N: {0}, R : {1}, R_2 : {2}, N_dash : {3}'.format(length_N, R, R_2, N_dash))
cr, mult_count = bin.multiply(c, R_2, mult_count)
#print('cr = c * R_2 = {0}'.format(cr))
#print('MR(c*R_2)の実行>>>')
large_C, mod_count, mult_count = MR(cr, mod_count, mult_count, N_dash, N)
print('largc_C = {0}'.format(large_C))
#print('MR({1}): large_C={0}'.format(large_C, cr))
large_M = large_C
array_d = bin.binary_d(d)
l = len(array_d)
for i in range(1, l):
mm, mult_count = bin.multiply(large_M, large_M, mult_count)
#print('MM = {0}'.format(mm))
#print('MR(M*M)の実行>>>')
large_M, mod_count, mult_count = MR(mm, mod_count, mult_count, N_dash,
N)
#MM_list.append(large_M // 100000000000)
#print('MR({1}) large_M={0}'.format(large_M, mm))
if array_d[i] == 1:
mc, mult_count = bin.multiply(large_M, large_C, mult_count)
#print('MC = {0}'.format(mc))
#print('MR(M*C)の実行>>>')
large_M, mod_count, mult_count = MR(mc, mod_count, mult_count,
N_dash, N)
#MC_list.append(large_M // 100000000000)
#print('MR({1}) large_M={0}'.format(large_M, mc))
#print('MR(M)の実行>>>')
bin.flag = 0
m, mod_count, mult_count = MR(large_M, mod_count, mult_count, N_dash, N)
#print('MR({1}) m={0}'.format(m, large_M))
print('countMM = {0}'.format(countMM))
print('countMC = {0}'.format(countMC))
print('countNG_MM = {0}'.format(countNG_MM))
print('countNG_MC = {0}'.format(countNG_MC))
return m, mod_count, mult_count, countMM, countMC, countNG_MM, countNG_MC
def MR(T, mod_count, mult_count, N_dash, N):
global countMM
global countMC
global countNG_MM
global countNG_MC
#global flag
#print('N: {0}'.format(N))
array_N = bin.binary_d(N)
length_N = len(array_N)
R = 2**length_N
#print('R: {0}'.format(R))
#print('N_dash: {0}'.format(N_dash))
R_2 = R * R % N
#print('N={0}, R={1}, R_2={2}, N_dash={3}'.format(N,R,R_2,N_dash))
#print(' ~~~~~~~~~~~~ MR(T:{0}, mod_count:{1}, mult_count:{2}, N_dash:{3}, N:{4}) ~~~~~~~~~~~~'.format(T, mod_count, mult_count, N_dash, N))
flag = bin.flag
tr, mod_count = bin.modulo(T, R, mod_count) # tr <= T % R の計算
#print('tr = T % R = {0} % {1} = {2}'.format(T, R, tr))
trn, mult_count = bin.multiply(tr, N_dash,
mult_count) # trn <= (T % R) * N'の計算
#print('trn = tr * N_dash = {0} * {1} = {2}'.format(tr, N_dash, trn))
m_1, mod_count = bin.modulo(trn, R,
mod_count) # m_1 <= ((T % R) * N') % Rの計算
#print('m_1 = trn % R = {0} % {1} = {2}'.format(trn, R, m_1))
mn, mult_count = bin.multiply(m_1, N, mult_count)
#print('mn = m_1 * N = {0} * {1} = {2}'.format(m_1, N, mn))
"""
質問その2：m_2計算時の「//」はmod_countをインクリメントしなくて良いか.
"""
m_2 = (T + mn) // R
#print('m_2 = (T + mn)//R = ({0} + {1})//{2} = {3}'.format(T, mn, R, m_2))
if m_2 <= N:
#print('MRにおいてmod_countを余分にインクリメントしませんでした.\n')
#print('@@@@@@@ flag = {0}'.format(flag))
#countNG += 1
#print('NO: countNG = {0}'.format(countNG))
if flag == 1:
countNG_MM += 1
#print('NO: countNG = {0}'.format(countNG))
#print('')
else:
countNG_MC += 1
#print('余分に剰余計算しなかった結果 = {0}'.format(m_2))
return m_2, mod_count, mult_count
else:
#print('MRにおいてmod_countを余分にインクリメントしました. m_2 = {0}'.format(m_2))
"""
質問その3：m_2 > Nのとき, mod_countを1インクリメントすべきかどうか.
"""
if flag == 1:
countMM += 1
#print('```````````````````````````countMM: m_2 = m_2 - N = {0} - {1} = {2}\n'.format(m_2, N, m_2-N))
#print('YES: countMM={0}'.format(countMM))
else:
countMC += 1
#print('///////////////////////////countMC: m_2 = m_2 - N = {0} - {1} = {2}\n'.format(m_2, N, m_2-N))
#print('YES: countMC={0}'.format(countMC))
mod_count += 1
#print('m_2 = m_2 - N = {0} - {1} = {2}\n'.format(m_2, N, m_2-N))
return m_2 - N, mod_count, mult_count
# # ModBinを実行するプログラム # import math import main import binary as bin p = main.p q = main.q N = main.N phi_N = main.phi_N array_N = bin.binary_d(N) length_N = len(array_N) R = 2**length_N R_2 = R * R % N countMM = 0 countMC = 0 countNG_MM = 0 countNG_MC = 0 MM_list = [] MC_list = [] # # N*(N') mod R = -1となるN'を返す. # """ def mod_equal_minus_1(N, R):