
RSa system
Recently, you and Sam have been playing the RSA encodingdecoding 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=3121915609(2)
1=31219(27)421,456(2)
1=27s2phi(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