Algorithm for binary less than in MPC
find the positions where $a$ and $b$'s bits differ: $c_i=a_i\oplus b_i=a_i+b_i-2a_ib_i$

compute partial or-sums: $d_{l-1}=c_{l-1},\quad d_i=d_{i+1}\vee c_i=a_i+b_i-a_i b_i$

isolate the first differing bit: $e_{l-1}=d_{l-1},\quad e_i=d_i-d_{i+1}$

the result is the corresponding bit in $b$: $\sum e_i b_i $