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crypto bugfixes

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dsa added (experimental)
This commit is contained in:
rnd 2018-05-19 11:54:56 +02:00
parent 1e2a9a76ae
commit 27e694ed5b
3 changed files with 244 additions and 41 deletions
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106
scripts/misc/crypto/bignum.lua
View File

@ -99,6 +99,70 @@ local exporthex_test = function()
end
--exporthex_test()
local base64c = {"A","B","C","D","E","F","G","H","I","J","K","L","M","N","O","P","Q","R","S","T","U","V","W","X","Y","Z",
"a","b","c","d","e","f","g","h","i","j","k","l","m","n","o","p","q","r","s","t","u","v","w","x","y","z",
"1","2","3","4","5","6","7","8","9","0","+","/"}
local base64n = {}; for i=1,#base64c do base64n[base64c[i]]=i-1 end
bignum.exportbase64 = function(n)
local binary = bignum.base2binary(n);
local base64 = bignum.binary2base(binary,64);
local data = base64.digits; local ret = {};
for i = #data,1,-1 do ret[#data-i+1] = base64c[data[i]+1] end
return table.concat(ret,"")
end
bignum.importbase64 = function(base64,newbase)
local digits = {}; local length = string.len(base64);
for i = length,1,-1 do digits[length-i+1] = base64n[string.sub(base64,i,i)] end
local base64 = bignum.new(64,1,digits);
local binary = bignum.base2binary(base64);
return bignum.binary2base(binary,newbase);
end
local base64_test = function()
local n = bignum.rnd(10,1,177);
say("B = " .. bignum.tostring(n))
local b64 = bignum.exportbase64(n);
say("B64 = " .. b64)
local m = bignum.importbase64(b64,10)
say("B = " .. bignum.tostring(m))
end
--base64_test()
bignum.exportascii = function(n) -- 32 - 127 (96) -- problem with non even base
local binary = bignum.base2binary(n);
local ascii = bignum.binary2base(binary,96);
local out = ascii.digits;
local m = 32;local ret = {};
for i = 1, #out do
ret[#ret+1] = string.char(m+out[i])
end
return table.concat(ret,"")
end
bignum.importascii = function(text,newbase)
local m = 32; -- ascii 32-127
local digits = {}; local j = 1;
for i=1, string.len(text) do
local c = string.byte(text,i)-m;
if c>=0 and c<96 then digits[j] = c; j =j +1 end
end
local ascii = bignum.new(96,1,digits);
local binary = bignum.base2binary(ascii);
return bignum.binary2base(binary,newbase);
end
local ascii_test = function()
local n = bignum.rnd(10,1,177); -- 512 bits
say("B1 = " .. bignum.tostring(n))
local ascii = bignum.exportascii(n);
say("ascii = " .. ascii)
local m = bignum.importascii(ascii,10)
say("B2 = " .. bignum.tostring(m))
end
--ascii_test()
-----------------------------------------------
-- ADDITION
-----------------------------------------------
@ -535,7 +599,7 @@ bignum.binary2base = function(n, newbase) -- newbase must be even
for i = #data,1,-1 do
bignum._add(ret,ret,ret) -- ret = 2*ret
out = ret.digits
out[1]=out[1]+ data[i]; -- if newbase is even no carry, else more complication here
out[1]=out[1]+ data[i]; -- WARNING: basically +1, if newbase is even no carry, else more complication here
end
return ret
end
@ -688,44 +752,4 @@ DH_bench()
-- note: DH security ( log problem ) can be solved for 512 bit by expert team, 1024 prime modulo for state actors ( logjam attack, "Imperfect Forward Secrecy:
-- How Diffie-Hellman Fails in Practice", Oct 2015
-- rnd key exchange v2 (improved key hide when doing verification):
-- auth + key exchange in one idea: A alice (client), B bob (server)
-- key generation: A generates its shared secret as v = g^x for secret random x and exchanges it with B.
-- this initial exchange can use DH with very large group to prevent any snooping.
-- verification:
-- 1. B picks random r and tells A y=g^r+v.
-- Note here that listeners only see g^r+v so they have no clue what v is or what g^r is. Even from multiple sessions they
-- learn nothing if g is generator of whole group and r truly random, since then g^r can be anything with same probability.
-- 2. A confirms identity by sending back hash(g^rx) = hash(v^r) = hash((y-v)^x) to prove you know a.
-- 3. shared secret is then another hash of K=g^rx = (g^r)^x = (g^x)^r.
--
-- basic idea is this: i tell you y=g^r for random r, you need to tell me y^x, so i believe you know x. But hide y by adding v and with hash so
-- listeners dont get any clues.
--observations:
-- 0. note that K lies in potentially smaller group generated by g^x, srp 6a is better here since for srp K = g^(b(a + ux)).
-- where a,b are random
-- The order of Z_p* is 2q for prime q, where p-1 = 2q ( p safe prime ). Order of g^x is either 2 or q or 2q (if (g^x)^2~= 1 then its not 2)
-- So order of g^x is still (p-1)/2 in this case.
-- thm: if G is finite group then order of any element divides |G|. Furthermore, if p is prime dividing |G| there exists element
-- in G of order p (cauchy thm)
-- 1. Suppose there is observer C. first time of interaction he can see v=g^x sent from A to B, but getting x is not possible ( log problem )
-- 2. later C can see B send v+g^r, and if he doesnt know v already this does not reveal it to him.. If we encrypt this this might introduce
-- weakness if not properly done, cause only good password would encrypt to number, bad password would be random mess.
-- WEAKNESS: if C knows v ...?
-- idea: first time exchange uses larger DH group for more safety to exchange: v = g^x to prevent C from learning x.
--srp v6a : http://srp.stanford.edu/design.html
--NOTE: srp v1 http://srp.stanford.edu/design1.html used weak approach to compute secret: S = (Wp*Xp)^Ys, where Xp = could be leaked
-- pass. verifier, Wp = controlled by client, Ys = random server secret
-- if rogue client know Xp he could select Wp so that Wp*Xp becomes value of his choice, hence controlling what the final shared secret
-- will be.
-- rnd key exchange v2 does not have that weakness. even if rogue learns v = g^x by other means he still needs to solve log problem for x.
-- prime generation: openssl prime -generate -bits 2048 -hex
self.remove() -- prevent loop in robot csm

132
scripts/misc/crypto/dsa.lua Normal file
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@ -0,0 +1,132 @@
--dsa by rnd
--digital signature algorithm
-- parameters: p,q,g
-- 1. p,q primes such that p-1 = a'*q, for example p safe prime, p-1=2q (N bits, L bits)
-- 2. select g in Z_p of order q ( for example 2^(p-1)/q or 3^... if first one is 1)
-- user keys: x in Z_q private key, y = g^x in Z_p = private key
-- MAIN IDEA: given message m and random k in Z_q and r = g^k %p %q find
-- w such that: g^(hash(m)*w + x*r*w) %p %q = g^k %p %q
-- this is easy if we know x -> solve w*(h+x*r) =k in Z_q -> w = (h+x*r)^-1*k in Z_q
-- now we hide k and x and show only y = g^x and r = g^k, problem is rewritten as:
-- PROBLEM:
-- g^(h*w) * y^(r*w) %p %q = r. So problem is determining such r and w.
-- NOTE: the idea of %p %q is to make brute force even slower, since:
-- x=y %p %q if x=y+t1*q+t2*p for some p,q
-- note :
--1 .the attacker doesnt have much freedom with h since he cant precisely control hash values
--2. suppose same k is reused for 2 different m. Write s = w^-1 mod q. Since
--s = k^-1*(h+r*x) mod q we get: s2 = k^-1*(h2+r*x) and s1 = k^-1*(h1+r*x),
-- or s2-s1 = k^-1( h2-h1) -> k = (s2-s1)^-1*(h2-h1).. and r^-1*(k*s-h)=x = BAD
-- must be careful that we pick very different k each time
-- 3. CAREFUL! k1 s1 = (h1+r1*x), k2 s2 =(h2+r2*x) -> k1 s1- k2 s2 - (h1-h2) = (r1-r2)*x.
-- so if we know there is little difference between k1,k2 we can try small sample different k2 and try to solve for x!
local bignum = _G.bignum
--512 bit
--c1d3a133c9b3720da868dda10b6a0bde0e1a47d797d3e02f2673157ad26c33970553352abd72114a48813b3f1a3d86120c2150d9c33780bf0ce31acf2e28b813
p = {base = 67108864, sgn = 1,digits = {36222995, 13022155, 782542, 57085150, 34349392, 42951044, 1291249, 4532514, 19578226, 29447373, 19317561, 30168555, 65023782, 32892404, 31515044, 2992175, 6872481, 14451562, 34815131, 198478}}
barrettp = {["k"] = 42, ["m"] = {["base"] = 67108864, ["sgn"] = 1,["digits"] = {28949715, 54423101, 2288892, 15960629, 25093079, 30961036, 9893219, 18572583, 6060506, 53345934, 62824245, 21175570, 51585074, 64634085, 50626132, 23908947, 34461644, 49242303, 44848557, 11882353, 4640537, 7818826, 338}}, ["n"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {36222995, 13022155, 782542, 57085150, 34349392, 42951044, 1291249, 4532514, 19578226, 29447373, 19317561, 30168555, 65023782, 32892404, 31515044, 2992175, 6872481, 14451562, 34815131, 198478}}}
q = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {51665929, 6511077, 391271, 28542575, 17174696, 55029954, 645624, 2266257, 43343545, 48278118, 43213212, 15084277, 32511891, 16446202, 49311954, 35050519, 3436240, 40780213, 17407565, 99239}}
barrettq = {["k"] = 42, ["m"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {50630993, 11411608, 4806431, 31921258, 50186158, 61922072, 19786438, 37145166, 12121012, 39583004, 58539627, 42351141, 36061284, 62159307, 34143401, 47817895, 1814424, 31375743, 22588251, 23764707, 9281074, 15637652, 676}}, ["n"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {51665929, 6511077, 391271, 28542575, 17174696, 55029954, 645624, 2266257, 43343545, 48278118, 43213212, 15084277, 32511891, 16446202, 49311954, 35050519, 3436240, 40780213, 17407565, 99239}}}
--2048 bit
--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
-- p = {
-- base = 2^26, sgn = 1,
-- digits = {62744243, 19635240, 60917474, 55456128, 37459655, 32447896, 55112955, 34207930, 51163200, 56246758, 55844124, 45401642, 36085928, 47437770, 20664880, 12411923, 54606930, 45153027, 5322668, 22132755, 15761415, 18473111, 8703875, 16094807, 6967620, 17763089, 31428929, 38041233, 4485332, 63963618, 11040321, 29265720, 51502910, 55331526, 63576425, 59745180, 16407094, 37040152, 6473027, 54882597, 8973561, 77317, 52363575, 21783671, 1991986, 48657866, 64847693, 43261383, 38561613, 7021085, 55608212, 4979958, 63470869, 2757076, 9303108, 61010659, 62048579, 50233028, 45339812, 24579835, 47993863, 51456822, 31033441, 34238847, 12003462, 13548658, 57544006, 26016612, 30031688, 22047781, 27180155, 41163470, 46927354, 66078116, 29634650, 62411651, 10819174, 14314285, 898854}
-- }
-- barrettp = {
-- ["k"] = 160, ["m"] = {["base"] = 67108864, ["sgn"] = 1,
-- ["digits"] = {52173231, 58926316, 7134135, 58005281, 29642925, 1996, 43704342, 19181367, 51834951, 40753938, 5670116, 25083444, 53681109, 39194353, 21018693, 16186348, 52641345, 34474171, 45582158, 65632598, 6663244, 17715531, 46582518, 715815, 35941432, 62741031, 14063905, 37500214, 33724930, 25815530, 29521098, 42349641, 30021354, 56331771, 20197595, 44642351, 39774, 15935544, 18538053, 54085894, 20262092, 170794, 877950, 7075184, 15922733, 42275553, 19627281, 61124663, 6351068, 20488035, 52369744, 26751026, 17905178, 25990200, 47243983, 42954366, 65859731, 23375626, 40610711, 9951837, 9139091, 55630155, 4911180, 17490059, 43409254, 37055369, 1417704, 12145177, 9055946, 41623298, 33230333, 1111792, 21966597, 20877280, 44498082, 6831928, 22418430, 4437100, 27282748, 12568457, 44322344, 74}}, ["n"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {62744243, 19635240, 60917474, 55456128, 37459655, 32447896, 55112955, 34207930, 51163200, 56246758, 55844124, 45401642, 36085928, 47437770, 20664880, 12411923, 54606930, 45153027, 5322668, 22132755, 15761415, 18473111, 8703875, 16094807, 6967620, 17763089, 31428929, 38041233, 4485332, 63963618, 11040321, 29265720, 51502910, 55331526, 63576425, 59745180, 16407094, 37040152, 6473027, 54882597, 8973561, 77317, 52363575, 21783671, 1991986, 48657866, 64847693, 43261383, 38561613, 7021085, 55608212, 4979958, 63470869, 2757076, 9303108, 61010659, 62048579, 50233028, 45339812, 24579835, 47993863, 51456822, 31033441, 34238847, 12003462, 13548658, 57544006, 26016612, 30031688, 22047781, 27180155, 41163470, 46927354, 66078116, 29634650, 62411651, 10819174, 14314285, 898854}}
local importsshprime = function(GH) -- use this to precompute all the needed prime stuff for extra speed
local base = 2^26;
local G1 = bignum.importhex(GH); local G2 = bignum.base2binary(G1);
local p = bignum.binary2base(G2,base);
code1 = minetest.serialize(p.digits) -- prime GH digits
local t = os.clock();
local barrettp = bignum.get_barrett(p);say(os.clock()-t) -- precompute barrett form
local code2 = minetest.serialize(barrettp)
local q = bignum.new(base,1,p.digits); q.digits[1] = q.digits[1]-1; bignum.div2(q,q); -- q = (p-1)/2
local code3 = minetest.serialize(q)
local barrettq = bignum.get_barrett(q); -- precompute q and this!
local code4 = minetest.serialize(barrettq)
local msg = "p " ..code1.."\nbarrettp " .. code2 .. "\nq " .. code3 .. "\nbarrettq " .. code4;
local form = "size[5,5] textarea[0,0;6,6;MSG;MESSAGE;" .. minetest.formspec_escape(msg) .. "]"
minetest.show_formspec("robot", form)
end
--importsshprime("c1d3a133c9b3720da868dda10b6a0bde0e1a47d797d3e02f2673157ad26c33970553352abd72114a48813b3f1a3d86120c2150d9c33780bf0ce31acf2e28b813")
DSA = {};
--msg = 520 bit number base 2^26
DSA.sign = function(msg,x) -- msg = (hash) message as number, x = private key
local m = 20; local base = 2^26;
local k = bignum.rnd(base,1,m); -- random value!
--warning: possible problem if q1.digits[1]-2 = 1-2<0 cause we didnt do carry! extremely unlikely, since digits in base 2^26.
local q1 = bignum.new(base,1,q.digits); q1.digits[1] = q1.digits[1]-2; -- q-2, needed to compute c^-1 = c^(q-2) mod q.
local g = bignum.new(base,1,{2^2}); -- g^q = 1 mod q ( g = 2^(p-1)/q mod p = 2^2)
local temp = bignum.modpow(g,k, barrettp); -- g^k mod p
local r = bignum.new(base,1,{});bignum.mod(temp,barrettq,r); --r = g^k mod p mod q
bignum.mul(x,r,temp); bignum._add(msg,temp,temp); -- temp = m+x*r
local temp1 = bignum.new(base,1,{});bignum.mod(temp,barrettq,temp1) -- range is very important, temp1 < q or modpow can freeze
temp = bignum.modpow(temp1, q1, barrettq); --(m+x*r)^-1 -- FREEZE PROBLEM if temp1>q. cause then temp1^2>q^2 and barret modpow fail..
local w = bignum.new(base,1,{});
bignum.mul(temp,k,w);bignum.mod(w,barrettq,temp1)
return {r,temp1} -- w = temp1 = (m+x*r)^-1*k in Z_q
end
DSA.verify = function(msg,sig,y) -- m = message, sig = {r,w} = signature, y = public key (= g^x)
-- CHECK: g^(m*w) * y^(r*w) %p %q == r
local m = 20; local base = 2^26;
local g = bignum.new(base,1,{2^2});
local temp1 = bignum.new(base,1,{});
bignum.mul(msg,sig[2],temp1); temp1 = bignum.modpow(g,temp1,barrettp); -- temp1 = g^(m*w) mod p
local temp2 = bignum.new(base,1,{});
bignum.mul(sig[1],sig[2],temp2); temp2 = bignum.modpow(y,temp2,barrettp); -- temp2 = y^(r*w) mod p
local temp = bignum.new(base,1,{});
bignum.mul(temp1,temp2,temp); bignum.mod(temp,barrettq,temp1); -- temp1 = g^(m*w) * y^(r*w) %p %q
return bignum.is_equal(temp1,sig[1])
end
dsa_sign_test = function()
local x = bignum.rnd(2^26,1,20) -- private key
local g = bignum.new(2^26,1,{2^2});
local y = bignum.modpow(g,x,barrettp) -- public key
local msg = bignum.importascii("hello world",2^26) -- will cut off at 520 bytes, use hash here for real thing
local sig = DSA.sign(msg,x)
--say(minetest.serialize(sig))
local ok = DSA.verify(msg,sig,y)
say(ok and "true" or "false")
end
dsa_sign_test()
self.remove()

47
scripts/misc/crypto/import_ssh_prime.lua Normal file
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@ -0,0 +1,47 @@
-- generate prime in openssl: openssl prime -generate -safe -bits 512 -hex
--512 bit
--c1d3a133c9b3720da868dda10b6a0bde0e1a47d797d3e02f2673157ad26c33970553352abd72114a48813b3f1a3d86120c2150d9c33780bf0ce31acf2e28b813
p = {
base = 2^26, sgn = 1,
digits = {36222995, 13022155, 782542, 57085150, 34349392, 42951044, 1291249, 4532514, 19578226, 29447373, 19317561, 30168555, 65023782, 32892404, 31515044, 2992175, 6872481, 14451562, 34815131, 198478}
}
barrettp = {
["k"] = 42, ["m"] = {["base"] = 67108864, ["sgn"] = 1,
["digits"] = {28949715, 54423101, 2288892, 15960629, 25093079, 30961036, 9893219, 18572583, 6060506, 53345934, 62824245, 21175570, 51585074, 64634085, 50626132, 23908947, 34461644, 49242303, 44848557, 11882353, 4640537, 7818826, 338}}, ["n"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {36222995, 13022155, 782542, 57085150, 34349392, 42951044, 1291249, 4532514, 19578226, 29447373, 19317561, 30168555, 65023782, 32892404, 31515044, 2992175, 6872481, 14451562, 34815131, 198478}}
}
--2048 bit
--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
p = {
base = 2^26, sgn = 1,
digits = {62744243, 19635240, 60917474, 55456128, 37459655, 32447896, 55112955, 34207930, 51163200, 56246758, 55844124, 45401642, 36085928, 47437770, 20664880, 12411923, 54606930, 45153027, 5322668, 22132755, 15761415, 18473111, 8703875, 16094807, 6967620, 17763089, 31428929, 38041233, 4485332, 63963618, 11040321, 29265720, 51502910, 55331526, 63576425, 59745180, 16407094, 37040152, 6473027, 54882597, 8973561, 77317, 52363575, 21783671, 1991986, 48657866, 64847693, 43261383, 38561613, 7021085, 55608212, 4979958, 63470869, 2757076, 9303108, 61010659, 62048579, 50233028, 45339812, 24579835, 47993863, 51456822, 31033441, 34238847, 12003462, 13548658, 57544006, 26016612, 30031688, 22047781, 27180155, 41163470, 46927354, 66078116, 29634650, 62411651, 10819174, 14314285, 898854}
}
barrettp = {
["k"] = 160, ["m"] = {["base"] = 67108864, ["sgn"] = 1,
["digits"] = {52173231, 58926316, 7134135, 58005281, 29642925, 1996, 43704342, 19181367, 51834951, 40753938, 5670116, 25083444, 53681109, 39194353, 21018693, 16186348, 52641345, 34474171, 45582158, 65632598, 6663244, 17715531, 46582518, 715815, 35941432, 62741031, 14063905, 37500214, 33724930, 25815530, 29521098, 42349641, 30021354, 56331771, 20197595, 44642351, 39774, 15935544, 18538053, 54085894, 20262092, 170794, 877950, 7075184, 15922733, 42275553, 19627281, 61124663, 6351068, 20488035, 52369744, 26751026, 17905178, 25990200, 47243983, 42954366, 65859731, 23375626, 40610711, 9951837, 9139091, 55630155, 4911180, 17490059, 43409254, 37055369, 1417704, 12145177, 9055946, 41623298, 33230333, 1111792, 21966597, 20877280, 44498082, 6831928, 22418430, 4437100, 27282748, 12568457, 44322344, 74}}, ["n"] = {["base"] = 67108864, ["sgn"] = 1, ["digits"] = {62744243, 19635240, 60917474, 55456128, 37459655, 32447896, 55112955, 34207930, 51163200, 56246758, 55844124, 45401642, 36085928, 47437770, 20664880, 12411923, 54606930, 45153027, 5322668, 22132755, 15761415, 18473111, 8703875, 16094807, 6967620, 17763089, 31428929, 38041233, 4485332, 63963618, 11040321, 29265720, 51502910, 55331526, 63576425, 59745180, 16407094, 37040152, 6473027, 54882597, 8973561, 77317, 52363575, 21783671, 1991986, 48657866, 64847693, 43261383, 38561613, 7021085, 55608212, 4979958, 63470869, 2757076, 9303108, 61010659, 62048579, 50233028, 45339812, 24579835, 47993863, 51456822, 31033441, 34238847, 12003462, 13548658, 57544006, 26016612, 30031688, 22047781, 27180155, 41163470, 46927354, 66078116, 29634650, 62411651, 10819174, 14314285, 898854}}
}
local bignum = _G.bignum;
local importsshprime = function(GH, base)
local G1 = bignum.importhex(GH); local G2 = bignum.base2binary(G1);
local G3 = bignum.binary2base(G2,base);
code1 = minetest.serialize(G3.digits) -- prime GH digits
local t = os.clock();local barrett = bignum.get_barrett(G3);say(os.clock()-t) -- precompute barrett form
local code2 = minetest.serialize(barrett)
local form = "size[5,5] textarea[0,0;6,6;MSG;MESSAGE;" .. minetest.formspec_escape("prime " ..code1.."\nbarrett " .. code2) .. "]"
minetest.show_formspec("robot", form)
end
GH = "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";
--GH = "bc614e" -> "12345678" -- chk ok
local code = importsshprime(GH,2^26)
self.remove()