N=1111010011000111 converts to octal: first, put the binary digits into 3s:
1 111 010 011 000 111 = 172307₈
Now convert to decimal:
172307
-2(using decimal arithmetic)
152
-30
1223
-244
9790
-1958
78327
-15664
62663=223×281.
So the decimal factors are 223 and 281.
Convert to octal:
223
22
+4(using octal arithmetic)
263
+54
337
281
28
+4
341
+70
431
These are 337₈ and 431₈ which convert to binary:
(a) 11011111 and 100011001 are factors in binary (223,281decimal).
e=11 (decimal), p=223, q=281, so N=pq=62663, (p-1)(q-1)=222×280=62160.
de=1 modulo (p-1)(q-1),
11d=1 mod 62160; 62161=5651×11+1, so 5651×11=1 mod 62160.
Therefore d=5651 and the private key is (62663:5651).
More to follow...