Question $2.$ Bob has sent a message e to Alice. Decrypt and decode Bob's

message. $($The standard ASCII encode and decode functions have been pro$-$

vided.$)($Hint: Sage will $($rightly$)$ object to switching mod$(f**e,q)$ to a number

modulo e$,$ since there is no natural homomorphism $\frac{Z}{q}Z\frac{Z}{e}Z.$ When you

need to do this, let $a\frac{?}{\text{I}}=nt$ eger$(mod(f**e,q))$ so that Sage now thinks of

this as a plain integer. You can then use a in your equation modulo g$.)$

def encode$($s$)$:

s $=$ str$($s$)$

if len$($s$)>71$:

print 'Error, string too long.$\text{'}$

return

return sum$($ord$($s$[$i$])*128^$i for i in range$($len$($s$)))$

def decode$($n$)$:

n $=$ Integer$($n$)$

v $=[]$

while n $!=0$:

v$.$append$($chr$($n $\%128))$

n $//=128$

return $\text{'}\text{'}.$join$($v$)$

q $=2227931092922619159088137825860917778654908962259364260724799634482871993679344024477214037820250089114550582112658547035427887568025339234287716719310475274676925427488455341264359399933469547884104546673995772201433027461094946187102932478528326005620630416132860562672779096576947422455142739470761$

f $=626346493922296891962453123852828762226840739369641575566811218944994465423391699556882442728756781708398121951194799184723646669035568862933089972532$

g $=977000403491994460922837866629768065514748480840502199588478427171542192931318741506250139746005024832848394512867819725451407771971457631489150320807$

h $=$ mod$($f$,$q$)^(-1)*$mod$($g$,$q$)$

e $=78718410001068529677588572614497505845736983903998613145157719609579915026054651042742971468860259386790104756141288441579114641145660779208031511331352898518118466155496980362017676866087191935146013866713673612565156506113920877930874410944039265560871107404980288749922814814885918909569495979623042532040822272019812413569842170256723818746065909730713382503129868557825346347038766126043524590160376367091553994881762361291104351498414443598243$