Which PhD field offers better job prospects: Math or Computer Science? I have completed my Master's in Mathematics.

I loved two subjects: Algebra (modules and non-commutative rings) and Cryptography (visual and algebraic).  I wanted to work on them in my PhD.  I scored good grades in both subjects.

Now when I am going to apply for a PhD program at different institutes.  I am getting two options PhD in mathematics and PhD in Computer Science where Algebra comes under Mathematics and Cryptography under CS.

Question:  Which PhD field offers better job opportunities in future: Math or Computer Science?
Assuming that you're interested in the private sector and holding all else equal, I'd guess that a Computer Science degree would tend to outperform a Math degree.  It's just such an incredibly useful field to have expertise in.

That said, if you're going for competitive research positions in overlapping fields, e.g. cryptography, then it may not matter that much so long as you have the appropriate background for that sub-field.  Then, you'll probably be evaluated against other applicants more heavily based on objective qualifications rather than the name that your degree has on it.