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In the fight against Covid-19, many governments and businesses are in the process of evaluating, trialling and even implementing so-called immunity passports. Also known as antibody or health certificates, there is a clear demand for any technology that could allow people to return to work and other crowded places without placing others at risk. One of the major criticisms of such systems is that they could be misused to unfairly discriminate against those without immunity, allowing the formation of an `immuno-privileged' class of people. In this work we are motivated to explore an alternative technical solution that is non-discriminatory by design. In particular we propose health tokens -- randomised health certificates which, using methods from differential privacy, allow individual test results to be randomised whilst still allowing useful aggregate risk estimates to be calculated. We show that health tokens could mitigate immunity-based discrimination whilst still presenting a viable mechanism for estimating the collective transmission risk posed by small groups of users. We evaluate the viability of our approach in the context of identity-free and identity-binding use cases and then consider a number of possible attacks. Our experimental results show that for groups of size 500 or more, the error associated with our method can be as low as 0.03 on average and thus the aggregated results can be useful in a number of identity-free contexts. Finally, we present the results of our open-source prototype which demonstrates the practicality of our solution.