Meaning of "integers modulo 4 " in "Fully homomorphic encryption modulo Fermat numbers" scheme
"Integers modulo 4" is usually the finite ring $(\Bbb Z_4,+,*)$ which internal laws are 

+ | 0 1 2 3     * | 0 1 2 3
--+--------     --+--------
0 | 0 1 2 3     0 | 0 0 0 0
1 | 1 2 3 0     1 | 0 1 2 3
2 | 2 3 0 1     2 | 0 2 0 2
3 | 3 0 1 2     3 | 0 3 2 1


but here, the question's citation only deals with the finite group $(\Bbb Z_4,+)$.




  difference between "integers" and "integers modulo 4"


In the later, everything is reduced to four values, which can be expressed on two bits, the two lower bits of normal integers.