It is quite easy to build MIRACL to work with Cygwin.

Basically follow the intructions in linux.txt, except first

(1) Copy mrmuldv.gcc to mrmuldv.c, and 

(2) Change the file linux to replace the line

as mrmuldv.s -o mrmuldv.o

with the line 

gcc -O2 -c mrmuldv.c

Then build the library and applications as usual with

$bash linux

(Make sure that the file "linux" has the correct Unix file format 
for CR/LF - not Windows format)