PurposeThe study jointly investigates sustainability and authenticity concepts in the food context during the COVID-19 outbreak with a fourfold objective: (1) understanding whether sustainability and authenticity are equivalent concepts in consumers' perceptions; (2) advancing knowledge on the role played by them about food frauds' perception; (3) investigating whether these concepts are considered as “risk relievers” by consumers, (4) comparing the concepts to understand which one has a greater weight on the consumer's perception.Design/methodology/approachThe study adopts a Combination of a Uniform and a shifted Binomial distribution (CUB models) on data gathered in Spain between June and August 2020 through an online questionnaire.FindingsThe findings reveal that: (1) consumers perceive sustainability and authenticity as different concepts in the food context and (2) as two important indicators of fraud protection of a product for consumers; (3) besides, authenticity is seen as a “risk reliever” in buying a food product, as well as sustainability, (4) although results underline high uncertainty in the latter case.Originality/valueBy considering that the COVID-19 outbreak seriously threatens food safety, security and nutrition, this research elucidates the relevant role of food sustainability and authenticity concepts as “risk relievers” in terms of food frauds and negative issues related to COVID-19.