diff --git a/5-rsa/alice.rb b/5-rsa/alice.rb index 422a367..cf13db3 100755 --- a/5-rsa/alice.rb +++ b/5-rsa/alice.rb @@ -14,31 +14,54 @@ load 'modul1.rb' sock = TCPSocket.new("localhost",3000) puts sock.gets + +starting = Process.clock_gettime(Process::CLOCK_MONOTONIC) + # Generate public and priv key def generateKeys + p = 0 + q = 0 + + pThread = Thread.new { while true - p = generatePrime(4096) - q = generatePrime(4096) + #p = random_gen_Zn(20,0) + p = generate(1024) + if primalityTest(p) + break + end + end + } - n = p * q - phi = (p-1)*(q-1) - - e = SecureRandom.random_number(0..phi) - - d = reciprocal_Phi_p(e,phi) - - if primalityTest(p) && primalityTest(q) && nwd(e,phi) == 1 && d > 1 + qThread = Thread.new { + while true + #q = random_gen_Zn(20,0) + q = generate(1024) + if primalityTest(q) break end end + } - return [n,e,d] + pThread.join + qThread.join + + n = p * q + phi = (p-1)*(q-1) + + while true + e = SecureRandom.random_number(0..phi) + d = reciprocal_Phi_p(e,phi) + if nwd(e,phi) == 1 && d > 1 + return [n,e,d] + end + end end keys = generateKeys n = keys[0] e = keys[1] d = keys[2] +puts "d: " + d.inspect pubKey = [n,e] privKey = [n,d] @@ -61,3 +84,7 @@ puts "Message: " + message.inspect # Close socket sock.close + +ending = Process.clock_gettime(Process::CLOCK_MONOTONIC) +elapsed = ending - starting +puts "Time " + elapsed.inspect diff --git a/5-rsa/modul1.rb b/5-rsa/modul1.rb index d878eec..aff56a9 100755 --- a/5-rsa/modul1.rb +++ b/5-rsa/modul1.rb @@ -13,6 +13,9 @@ require 'prime' require 'thread' def nwd(a, b) + if a == 0 + return false + end b == 0 ? a : nwd(b, a.modulo(b)) end @@ -26,26 +29,31 @@ def extended_euklides(a, b) end # Zad. 1.1 -def random_gen_Zn(n,k) - if 2**(k-1) < n && k > 0 - if k == 1 - min = 0 - max = 1 - else - min = 2**(k-1) - max = (2**k)-1 +def random_gen_Zn(k,n) + + if n == 0 + n = 2 ** k + end + + if k == 1 + max = 1 + else + kb = k.to_s(2) + minimum = [] + minimum << 1 + k = kb.length - 1 + + while (k != 0) do + j = SecureRandom.random_number(2) + minimum << j + k = k - 1 + end + min = minimum.join.to_i(2) + max = n - 1 + if min < max + return SecureRandom.random_number(min..max) end end - - while true do - r = SecureRandom.random_number(min..max) - if r < n - break - end - end - - return r - end # Zad. 1.2 @@ -66,19 +74,21 @@ def betterExponentiation(x,k,n) return false end - b = k.to_s(2).reverse - l = b.count "[0-1]" - y = 1 - i = l - 1 + if x < n && x > 0 + b = k.to_s(2).reverse + l = b.count "[0-1]" + y = 1 + i = l - 1 - while i >= 0 - y = y**2 % n - if b[i]=="1" - y = y * x % n + while i >= 0 + y = y**2 % n + if b[i]=="1" + y = y * x % n + end + i = i - 1 end - i = i - 1 + return y end - return y end # Zad. 1.4 @@ -110,7 +120,7 @@ def primalityTest(n) return true end - counter = 10 + counter = 20 while (counter != 0) do b = SecureRandom.random_number(2..n-2) # Tez dziala n-1 if betterExponentiation(b,n-1,n) != 1 @@ -121,25 +131,25 @@ def primalityTest(n) return true end - -def randomNumber(k) - randomNumberArray=[] - randomNumberArray << 1 - k= k - 1 - - while (k !=0 ) do - j = SecureRandom.random_number(2) - randomNumberArray << j - k = k - 1 - end - return randomNumberArray.join.to_i(2) -end - def specyficPrimaryNumber + p = 0 + q = 0 + + qThread = Thread.new { + while true + q = SecureRandom.random_number(2 ** 256) + if primalityTest(q) + break + end + end + } + + qThread.join + while true do q = SecureRandom.random_number(2 ** 256) p = 2 * q + 1 - if primalityTest(q) && primalityTest(p) + if primalityTest(p) return p,q end end @@ -156,85 +166,6 @@ def generator(p,q) end end -def generatePrime(n) +def generate(n) return `openssl prime -generate -bits '#{n}'`.gsub(/\n$/, '').to_i -end - -################################################################################### - -# Zadanie.1 Losowy element z zbioru Z_n -# -# Uzycie funkcji: -# random_gen_Zn(n,k) -# -# Gdzie n - grupa mod -# k - ilosc bitow - -#puts "Zadanie 1: " + random_gen_Zn(2817960879631397637428637785383222308241674912977296371078328827783823173932945686560271709717223685413005001487628305095704070793958971415087255523073935114518202433817141315589046697665767753020703330561718642810157214393228915238808369985314803605127547366769525321238034444131545038866079220135011303234308583293055538438855440051375449844277218217712896675378963068720345515473434111699867542985885331741594726201346190830240692715577811297545617592986841862266976883958728343753502720654957572591625318922387371348775299617016576604164586635463962864505536324347369114225605202600072081219902252264258236028218613372215876496394341867072862629022156295534655310094481486891656868251869749451857161662890356600101860594118885136794555465318782343870373413707643678756555809662335374658562880045543430140169913540153961566294704894163494226738977413711366121112146042996377423578488354012607979075727403258666348434920910981957617905109649522084109820427893425361930683246183514216962034556016051184044970184676662827978420213281480510069379347007543973139554178175690773315927469361215139519543395792659825942864347234234285907203635728345512501417615714291999748745375110198782386769755218587158953598215023147871490893052124457996091330393194346889440433647348345868290410045628941650640315817691074244257070087501412656465257388504574920756736653658826614297081956072241319983753399595743495837950519045870810249068878008938965513649172515852388457433200750100902751828486806189811961720524504976040165319005498382580099718522287255514024665802127411452771343820848551192190973237603226514162458911052832006635099614443220118029822801995173084006448848714642581145597450095993844936566471047767974285413266855493150984091512278787539020882065620089396507786047199321023827465489494495513119543424285384803025749486259267450477917340669954258887755716092814959537213397128776047910200001947756249766479670986137076981224642743069725401099384031028670810757683522821674118926373517718330706064178699035286815124318059529948663730575377063300582239742709428517028624628630255640464009691179606104444672232047869709734836046571505598681429286372976726889778746623725623485244272247797117303046464791441413956650048631706362550020890628552166104678993837549091779514727408814458173452235187339390489070470959043964826221641981413639067723526075949807992319555177364587831440901887979371647118775640122112691496917328672989185787786333743943571201682455849788768447941052589112093217146238196393058840427167875379895033862665036580869700901671149307822867600084775797450043528335040523181300939047560092173656437964805986878846909755616898664300908149121103065456346895895553346803762232995496756924185713587688989499627282573083392504068537865838813511676470822568313458216527495376958238195629276140142912559084213140117194512209752564237149304569698487234268004667685663277598956964116311211220970915272172182795014191615102024324085452311963348372375839824417067170842114940446271152850552864783993722225100122068507428533164772669151799555291529447719732682260868021763685052338407930046892500473287361324180925326385131283404240275852188687583358717018916949107259963059221294732376067807306008309012964676038322426438467806570485299377626514669181680963962016304313021681669696580753784295259640169007074506637844332833804045109981978476343942218065708022217566222881348496310403404164467438352649885637702780969376650799749541038736604262724814821757258372470336571211357167468680200965241152364670892328226187787108777323221988154289834826302745446444518424440700033948649807665278475079826664974213162552336459719975478725157313669922561440432360473265250572606571269284353534676478375363478936179040075297456773814344907213125333476476655366455733030460908712160208004620689954788191597043073132610377893018543064926955781952650214504633097216561549411315119718460509357878230720821699669794678584993658379092808863297233433557739623968183417003317301945898487820593437670555891465841469699644209269444311251317668652989906375182749637967733151694853436985266479700749763565024494627271013468757521359567838089899510388135209838269214753262972848939363295323913595985611694315406247934779335196977854974497594863447427077079600386381593134665326520126544264832044936966738225526176229232138173609626231926255343974851041449136902209592667970872917688005523210617825501923851244940494708102661449185546240415803793231334092660117374732910436571816210806786100000371385219128407888245069151381708001509375,15000).inspect - -################################################################################### - -# Zadanie.2 Odwrotnosc w grupie Phi(n) -# -# Uzycie funkcji: -# reciprocal_Phi_p(n,p) -# -# Gdzie p - element w grupie phi -# n - liczba nalezaca do N - -#puts "Zadanie 2: " + reciprocal_Phi_p(10,13).inspect -#puts "Zadanie 2: " + reciprocal_Phi_p(76638723687263876287368268368726378623873687326872634868374687236487623874687648634863847623846834687643,100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000961 ).inspect - -################################################################################### - -# Zadanie.3 Efektywne potegowanie. -# -# Uzycie funkcji: -# betterExponentiation(x,k,n) -# -# Gdzie obliczna jest wartosc x^k mod n - -#puts "Zadanie 3: " + betterExponentiation(823789137891789217389173981378913789137289,565490994747691690475378499398697660773449981085993539792067,1399661509700116309409184866497198118594638278433610469383879).inspect -#puts "Zadanie 3: " + betterExponentiation(8,2,30).inspect -#puts "Zadanie 3: " + betterExponentiation(76638723687263876287368268368726378623873687326872634868374687236487623874687648634863847623846834687643, 76382637812836812638612836812638612376182263812623861283618723681263861238612386, 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000961).inspect - - -################################################################################### - -# Zadanie.4 Sprawdzenie czy element a jest reszta kwadratowa w Z_p -# -# Uzycie funkcji: -# remSqEuler(a,p) -# -# Gdzie a - element -# p - liczba pierwsza - -#puts "Zadanie 4: " + remSqEuler(4,15485863).inspect -#puts "Zadanie 4: " + remSqEuler(3,13).inspect -#puts "Zadanie 4: " + remSqEuler(5,13).inspect - -################################################################################### - -# Zadanie.5 Obliczanie pierwiastka kwadratowego w ciele F_p*. -# -# Uzycie funkcji -# squareRootFp(p,b) -# -# Gdzie p - liczba pierwsza (modulo) -# b - reszta kwadratowa - -#puts "Zadanie 5: " + squareRootFp(15485863,2).inspect - -################################################################################### - -# Zadanie 6. Test pierwszości. -# -# Uzycie funkcji: -# primalityTest(n) -# -# Gdzie n - liczba wejsciowa - -#puts "Zadanie 6: " + primalityTest(13).inspect -#puts "Zadanie 6: " + primalityTest(100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000961).inspect - -################################################################################### +end \ No newline at end of file diff --git a/5-rsa/rsa.rb b/5-rsa/rsa.rb new file mode 100755 index 0000000..f181c60 --- /dev/null +++ b/5-rsa/rsa.rb @@ -0,0 +1,89 @@ +#!/usr/bin/ruby + +###################################### +# +# Marcin Woźniak +# s434812 +# +##################################### + +load 'modul1.rb' + +def generateKeys + p = 0 + q = 0 + + pThread = Thread.new { + while true + p = generate(4072) + if primalityTest(p) + break + end + end + } + + qThread = Thread.new { + while true + q = generate(4072) + if primalityTest(q) + break + end + end + } + + pThread.join + qThread.join + + n = p * q + phi = (p-1)*(q-1) + + while true + e = SecureRandom.random_number(0..phi) + d = reciprocal_Phi_p(e,phi) + if nwd(e,phi) == 1 && d > 1 + puts + puts "p: " + p.inspect + puts "q: " + q.inspect + return [n,e,d] + end + end +end + +starting = Process.clock_gettime(Process::CLOCK_MONOTONIC) + +keys = generateKeys +n = keys[0] +e = keys[1] +d = keys[2] +#n = 71080843952579821536808659073592377254223354771744338571962856057130579776693987295676130693029061514639099711984974088368385378005316058780753506803821677092757604732237641915894898542024389645033816194122765899995205755268676569966322474451123277045758957825791521431858660785814981788128816934481845228865657975621955459104448356520475723668712159918538393669309901176250743549048998632825755599078853414670244789822627531750788254524608995657662504492295387636179849501161984714800687072140115145090431501734806775267531078231806454936476311362413330800768637545279561130577224924702796746010760553 +#e = 8568635405550720312742658917750002897800817834357945962764047863500567259665199816353662868482237115378064375549642009491300055266130153886053132983796459461609268298948099540540738951524519496677791059134156506559882797235730790145589763065725951828812878626920288539460548881334613744784835397042451 +#d = 32386335677908137318863892465199815383071366385532868349312560590843149093721116637041180595846942643803479043836883315885718155256027682010626277652945965025765385727195326719478281847964209269755614625652671779134510726553430069309309313886139982070647506703881883189451691281061102384111546214788607921485198991338966374053889616005762912361311568996467325682971499059915979784926145499607252111375306393358879385624365652331679677612939527522511050610059838669634395550442681215662470714984216749116088717552501057409391377221576136360347218774125110880473654893374271141612063430957777800926156251 +pubKey = [n,e] +privKey = [n,d] +message="1234" + +if message.to_i > n.to_i + return "error" +end + +cipher = betterExponentiation(message.to_i,e.to_i,n.to_i) +decryptedMessage = betterExponentiation(cipher.to_i,d.to_i,n.to_i) + +puts +puts "pubKey Alice: " + pubKey.inspect +puts "privKey Alice: " + privKey.inspect +puts +puts "Message: " + message.inspect +puts +puts "Cipher: " + cipher.inspect +puts "Decrypted Message: " + decryptedMessage.inspect +puts +#puts +#puts +#puts "n=" + n.inspect +#puts "e=" + e.inspect +#puts "d=" + d.inspect + +ending = Process.clock_gettime(Process::CLOCK_MONOTONIC) +elapsed = ending - starting +puts "Time " + elapsed.inspect \ No newline at end of file