A branch of the Ministry of Defence is funding postgraduate research into the culture of computer hackers, crowd behaviour at music festivals and football matches, and the impact of Twitter, Facebook and online conspiracy theories in times of crisis.

The MoD's Defence Science and Technology Laboratory (DSTL) pays six-figure sums to support individual PhD students to help understand the rapidly evolving world of cyberspace and the way in which social media have become an integral part of daily life.

While some of the PhD projects in the £10m programme have conventional military applications – such as researching technology to support underwater drones, and the development of clothing with fully embedded electronics – £97,487 of funding for research at King's College London into "the rise of the digital insurgency" is typical of the new direction.

Background papers for the digital insurgency doctorate at King's College say that the research will target the so-called "hacktivist" group Anonymous. The project will involve the researcher aiming to interact with members of Anonymous, addressing "known unknowns" relating to the group, and understand its grievances and goals, why people are attracted to it and its internal politics.

Rather than just focusing on hacktivism, however, the DTSL appears to be taking an increasing interest in broader issues of social media and online behaviour too. In February, it will host an invitation-only conference focused on "social influence in the information age".

Other PhD projects funded include one at the University of Exeter, which receives £82,630 from the DSTL, entitled Collective Action in the Digital Age: Social identities and the influence of online and offline behaviour.

Picking out the role of Twitter, Facebook, Skype and mobile messaging, a contract for the project states: "The events of the Arab spring, the London student protests or the summer 2011 riots in English towns and cities show the importance of understanding synchronised collective actions driven by online interactions."

The project aims to "deliver new and innovative ways to understand and influence online behaviour".

Mark Levine, a professor of social psychology who is supervising the Exeter PhD, told the Guardian: "I think [the MoD] are interested in online influence. That is why they have put money into this kind of stuff. They want to know what influences people, when and how.

"They are interested in influences which might promote what, from their point of view, might be antisocial stuff that they might want to stop, but they are also interested in the kinds of things they can do to promote situations where groups themselves prevent things they are worried about online."

Levine, who has been a working with others to demonstrate how groups can reduce violence or promote pro-social behaviour, added that the idea behind the project was to test, in an online environment, the psychological theories about why people behave collectively in the way they do offline, such as in football crowds.

The MoD initiated a national PhD sponsorship scheme in 2011, with the intention that successful bidders for the support would also spend time at the DSTL, "subject to certain caveats", according to the agency. Researchers in a wide range of disciplines have been provided with hundreds of thousands of pounds of funding across a range of applications.

How technology can be used to wield influence is also the focus of a £137,433 PhD programme at Queen Mary, University of London, called "Analysing and influencing crowd behaviours through arrays of ad-hoc mobile sensors". Mobile sensors typically include the digital compasses that are used in modern mobile phones for mapping, but which can also be used to identify the location and activities of their owner.

The contract states: "The PhD student will gather large-scale datasets from a variety of different mass crowd events, such as music festivals, sporting events, etc."

It adds that the research will aim to "provide essential tools for event planners and event monitors for wide ranges of events, planned (festivals, football matches, political rallies) or ad hoc (riots, protests)."

Techniques to be explored will include "targeting influential individuals" and crowdsourcing.

Elsewhere, £139,649 is being channelled to another Queen Mary PhD called "Cross-cultural attitudes and the shaping of online behaviour in crisis situations". It aims to examine trends and patterns relating to the flow of information on social media during events such as terrorist attacks and natural disasters.

Course organisers say it will "look at how news production is mediated by first-hand accounts through social media platforms such as Twitter and, secondly, how crisis situations foster the setting-up of dedicated platforms for communion and their function in mediating trauma as well as in endorsing or rejecting dominant commentaries (including conspiracy theories and propaganda) in mainstream media".

A Queen Mary spokesperson said that as part of the research, small pilot studies had been conducted at a music festival and at internal gatherings, but seeking ethical approval and participant recruitment would begin for large-scale events in 2014. The spokesperson said that the research would examine the impact of incorrect information in transport and disaster situations as well as music festivals. "All research on human subjects at Queen Mary is subject to ethical review. Furthermore all data was gathered and will be gathered with the informed consent of the participants."

The spokesperson added: "For festivals, we are looking at gathering information in order to provide participants with interesting topographical information such as 'fun' or crowdedness. This research will collect data that will provide essential information on crowd dynamics of such events."

Other PhDs benefiting from military financial aid include: "Exploring identity within modern technology – the influence of social and ethnical concerns on models of distributed identity" (£107,012, the University of Southampton); "Achieving legitimacy in a new media ecology" (£85,588, University of Glasgow); "Data mining to understand international dimensions to online identity – a classification of 2+billion names and their linkage to virtual identities and social network traffic" (University College London £106,160); and "Social movement 2.0: collective identity in the era of online participatory media" (Kings College London, £97,486).Jim Killock, executive director of the Open Rights Group, said: "Clearly there is a range of things which the security services already do.

"There is often a strong case for moves in this direction to be tempered by some very hard thinking about the ethics of these questions and the risk of legitimate policing slipping, potentially, into being attempts to control and influence.

"Obviously, the nature and type of the mass surveillance which we now know that the NSA and GCHQ engaged in was simply not legitimate.

"But the fact is that digital information will increase. What has to also increase alongside it is transparency and oversight. We have not really had that debate and the fact that we should be taking note and looking at the potential use of research such as this is entirely appropriate."

Nick Pickles, director of Big Brother Watch, said: "People will rightly want to know why the Ministry of Defence is investing in research that clearly carries significant privacy implications. These areas of research also highlight how badly in need of reform the wider legal framework governing surveillance activities is, particularly given the apparent interest in using social networks and internet-connected sensors to track and analyse people.

"The department needs to be much more transparent about why it is funding so much of this research if the public are to have confidence that it does not threaten our civil liberties and that the military's surveillance capabilities are not to be turned on British citizens."

An MoD spokesperson said: "Cyber-security is an issue of growing importance. As routine cyber-security measures (patching, anti-virus) become ubiquitous, socially engineered attacks are a growing threat.

"DSTL seeks to understand these threats and the vulnerabilities they exploit in order to provide effective advice and support to the MoD and wider government on defending against these threats."

The spokesperson added that the MoD was also "trying to understand the world in which we live and anticipate the world in which we will live" and that to do so "it now needs to incorporate an understanding of events in cyberspace and how they might unfold".