#GLORIA LIU, Apr 20 2024, Assignment 24

read `C24.txt`:

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#1. Decide whether you would like to sign up for the annual field trip to the Princeton cemetery followed by a free dinner.
#{}

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#2. Generalize AliceToBob(M,Nbob,eBob,Nalice,dAlice,H) and BobReadAlice(MS,Nbob,dBob,Nalice,eAlice,H) to
#AliceToBobG(ListM,Nbob,eBob,Nalice,dAlice,H) and BobReadAliceG(MS,Nbob,dBob,Nalice,eAlice,H) (where MS=[ListM',S]),
#where ListM is an arbitrary list of integers each between 1 and Nbob, and the signature is the sum of the integers in 
#ListM cubed mod H. The encrypting and descryting is done separately for each member of ListM.

AliceToBobG:=proc(ListM,Nbob,eBob,Nalice,dAlice,H) local m,ListM1,m1,x,S:
ListM1:=[]:
x:=0:
for m in ListM do
 m1:=m&^eBob mod Nbob:
 ListM1:=[op(ListM1), m1]:
 x:=x+m mod H:
od:
x:=x&^3 mod H:
S:=x&^dAlice mod Nalice:
[ListM1, S]:
end:

BobReadAlice:=proc(MS,Nbob,dBob,Nalice,eAlice,H) local m1,m,ListM,ListM1,S,x,x1:
ListM1:=MS[1]:
S:=MS[2]:
ListM:=[]:
x:=0:
for m1 in MS do
 m:=m1&^dBob mod Nbob:
 ListM:=[op(ListM), m]:
 x:=x+m mod H:
od:
x:=x&^3 mod H:
x1:=S&^eAlice mod Nalice:
if x1<>x then
 RETURN(FAIL):
fi:
ListM:
end:

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#3. Look at the class mailing list and find the three students right after you
#Email them your public ([N,e]) part of your public key (but keep d to yourself). Also email them your public H (so the 
#Hash function is M^3 mod H)
#Ask them to email you THEIR [N,e] but to keep their d to themselves.

key:=MakeRSAkey(20,10);
H:=nextprime(rand(10^10..10^11)());

#key := [249846258933717282231658119892328072250259,57885386393133504599689153013392340889181,108767995984135205057484974537235722651557]
#H := 67646025787

#I sent the correct message and signature to Nkhalo, [1361451599237996173775, 63408949518079727907542252003102021972084] using the public key N := 2111365616595924973189 e := 332986169625729448079. He was able to decode it correctly. 
#I sent the correct message and signature to Lucy, [1609714563803922791728, 63408949518079727907542252003102021972084] using the public key N=1883925284252198456411 e=489703529340811966481. 
#I received [127194014635818882616264466777093555824061, 867633009183092191876] from Joseph and was able to find his birthday (6122003). 
#Update: I received [220212942073894330003834774776685565211173, 298332590935502338435285101982783606776542] from Nuray and was able to find her birthday (8042003).