Recently, you and Sam have been playing the RSA encoding-decoding game with the
same evaluations for the letters as in the examples (00 for blank, 01 for letter \a", ..., 26 for letter \z"), with s = 31; 219 and N = 422; 767 (which factors as N = 569*743). Now
Sam sends you an encoded message E = 88; 588 with a hint a University in this area".
Which university is it?
I started by finding phi(N)=421,456
Then I found t
421546=31219(13)+15609
31219=15609(2)+1
1=31219-15609(2)
1=31219(27)-421,456(2)
1=27s-2phi(n)
27s=1mod(phi(n))
so t=27
Now I began decoding with M=E^t (modN)
I noticed 27=2^4+2^3+2+2^0
E=88588 mod N
E^2=9923 mod N
E^(2^2)=383985 mod N
E^(2^3)=261305 mod N
E^(2^4)=50389 mod N
so we have M=(50389)(261305)(9923)(88588) mod N
It's this final part of breaking this down that I'm struggling with