Cybersecurity is a global phenomenon representing a complex socio-technical challenge for governments, but requiring the involvement of individuals. Although cybersecurity is one of the most important challenges faced by governments today, the visibility and public awareness remains limited. Almost everybody has heard of cybersecurity, however, the urgency and behaviour of persons do not reflect high level of awareness. The Internet is all too often considered as a safe environment for sharing information, transactions and controlling the physical world. Yet, cyberwars are already ongoing, and there is an urgent need to be better prepared. The inability to frame cybersecurity has resulted in a failure to develop suitable policies. In this paper, we discuss the challenges in framing policy on cybersecurity and offer strategies for better communicating cybersecurity. Communicating cybersecurity is confronted with paradoxes, which has resulted in society not taking appropriate measures to deal with the threats. The limited visibility, socio-technological complexity, ambiguous impact and the contested nature of fighting cybersecurity complicates policy-making. Framing using utopian or dystopian views might be counterproductive and result in neglecting evidence. Instead, we present evidence-based framing strategies which can help to increase societal and political awareness of cybersecurity and put the issues in perspective.