Recruiter Asked for Last 4 SSN and Birthday (MM/DD)

I applied for a job on Dice.com and I got an email back from the recruiter requesting some information that I am pretty skeptical about giving out. Specifically the last 4 of my SSN and my birthday (MM/DD). Should I respond to this recruiter with the information he requested? Or is this is scam?

Email body:

Hi (redacted),

Please send me following details. Thank you.

Full Name:

Phone:

Email:

Location:

Willing to relocate to client place:

Work Authorization:

Last 4 digits of SSN:

Pay Rate:

MM/DD of Birth:

LinkedIn:

Availability

Professional References:

​

For the record, the company is a recruiting company called Kyyba. I couldn't find much information on people who have worked with them to find a job.

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