Hmmn.. Off the top of my head it looks like an encryption
Algorithm..... RSA mayhap?
This looks like either RSA or the Cayley Purser algorithm..
jeremy
-----Original Message-----
From: Cary Gordon [mailto:[EMAIL PROTECTED]]
Sent: Tuesday, October 03, 2000 3:37 PM
To: CF-Talk
Subject: OT: Harder Math Question
Any idea of how I can turn this algorithm a custom tag? It is in
Mathematica format as that is the only way I could think of to post it here.
StringToMatrices[text_String]:= Partition[Parition[Flatten
[Append[StringToList[text],{32,32,32}]],2],2]
_______________________________________________________________
MatriceToString[l_List] :=
StringJoin [ ConvertNumber/@Flatten[1]]
_______________________________________________________________
CPpqn[digits_Integer] :=Module[{
p1 = FirstPrimeAbove[Random[Integer,
{10^(Floor[digits/2]-1), 10^(Floor[digits/2])-1}]],
q1 = FirstPrimeAbove[Random[Integer,
{10^(Floor[digits/2]-1), 10^(Floor[digits/2])-1}]],
While[PrimeQ[p = 2p1 +1], p1 = FirstPrimeAbove[p1 + 1]]; p;
While[PrimeQ[q = 2q1 +1], q1 = FirstPrimeAbove[q1 + 1]];
q; n = pq; ]
_______________________________________________________________
randmatrix := (Catch[
Do[m = Table[Random[Integer, {0, n}], {i, 1, 2}, {j, 1, 2}];
If[GCD[Mod[Det[m], n], n] == 1, Throw[m]], {1000}]])
_______________________________________________________________
inv[a_] := (d = Mod[Det[a], n]; i = PowerMod[d, -1, n];
{{Mod[i * a[[2, 2]], n], Mod[-i * a[[1, 2]], n]},
{Mod[-i * a[[2, 1]], n], Mod[i * a[[1, 1]], n]}})
_______________________________________________________________
mmul[j_, k_] := Mod[
{{Mod[j[[1, 1]]*k[[1, 1]], n] + Mod[j[[1, 2]]*k[[2, 1]], n],
Mod[j[[1, 1]]*k[[1, 2]], n] + Mod[j[[1, 2]]*k[[2, 2]], n}},
{Mod[j[[2, 1]]*k[[1, 1]], n] + Mod[j[[2, 2]]*k[[2, 1]], n],
Mod[j[[2, 1]]*k[[1, 2]], n] + Mod[j[[2, 2]]*k[[2, 2]], n]}},
n]
_______________________________________________________________
CPparameters := (identity = {{1, 0}, {0, 1}};
alpha = randmatrix; Catch[Do[chi = randmatrix;
If[mmul[chi, alpha] ! = mmul[alpha, chi],
Throw[chi]], {10000000}]]
chiinv = inv[chi]; alphainv = inv[alpha];
Catch[Do[s = Random[Integer, {2, 50}];
gamma = Mod[MatrixPower[chi, s], n];
If[gamma != identity, Throw[gamma]], {10000000}]];
Catch[Do[delta = Mod[Mod[Random[Integer, {1, n-1}]gamma, n]
+ Mod[Random[Integer, {1, n-1}]identity, n], n]
If[delta !=identity &&
mmul[delta, alpha] !=mmul[alpha, delta], Throw [delta]],
{10000000}];
beta = mmul[mmul[chiinv, aphainv], chi];
deltainv = inv[delta];
epsilon = mmul[mmul[deltainv, alpha], delta];
kappa = mmul[mmul[deltainv, beta], delta];
lamda = mmul[mmul[chiinv, epsilon], chi];)
_______________________________________________________________
CPenc[plain_String] := CPencNum [ StringToMatrices[plain]]
_______________________________________________________________
CPDecNum[l_list] := Table[mmul[mmul[lamda, l[[i]]], lamda], {i,
Length[l]}]
_______________________________________________________________
CPEncNum[l_List] :=
Table[mmul[mmul[kappa, l[[i]]], kappa], {i, Length[l]}]
_______________________________________________________________
CPdec[cipher_List] := MatricesToString[CPDecNum[cipher]]
I will award a meaningful, albeit insignificant, prize to the first poster
who can identify, even in broad terms, the (quite useful) function of this
algorithm.
Cary
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