But it rejected any notion there was a skills shortage at the secretive agency, which is a member of the shadowy Five Eyes intelligence alliance.
"We want more people to be thinking of the GCSB as a possible career path," Hampton said.
"It's clear to me from talking with universities and students across the country that many people aren't aware of the types of careers that subjects like mathematics can actually lead to."
Hampton said the GCSB offered a range of career paths, such as engineering, cyber security specialists, computer science and technical analysis.
"The work we do is incredibly interesting and no two days are the same."
With a Budget boost, the GCSB was continuing to grow its staff, with a focus this year on more women with science, technology, engineering and mathematics (STEM) backgrounds.
The agency was again offering four $10,000 tertiary scholarships to women studying STEM subjects at New Zealand universities, in a push to attract them to cyber-security.
The GCSB ran a graduate programme that offered places to around 20 graduates each year.
"Diversity is proven to lead to better decision-making which is important for an organisation such as ours," Hampton said.
"The GCSB is also working to reduce its gender pay gap by half; we've set a target of five per cent by 2021."
But of course, not everyone could chuck their CV in the post.
Any job in the intelligence community required candidates to have been a New Zealand citizen for at least 10 years; a holder of permanent residence; or a holder of a current New Zealand residency class visa with citizenship for at least 10 years in one of the other four Five Eyes countries: the UK, US, Canada and Australia.
And then there was being able to get "Top Secret Special" security clearance.
"Ordinarily to obtain this level of clearance candidates must have a 15 year checkable background in countries where meaningful and reliable checks can be undertaken," vacancy notices state.
Hampton said the GCSB had two main missions: protecting our most important organisations and infrastructure from cyber-attacks, and collecting electronic intelligence "in line with the Government's priorities".
"Our goal is to deliver quality security and intelligence services, underpinned by a high level of public trust and confidence."
Five perks of working at our spy agency
• "A supportive and flexible environment that encourages personal growth"
• "Career development opportunities and a commitment to learning and development"
• "A family friendly approach to employment, including a childcare subsidy depending on your situation"
• "An active and energetic social club" and "an in-house gym and showers"
• "Health insurance and generous vision care benefits"
Source: Government Communications Security Bureau