Increased Resilience in Threshold Cryptography: Sharing a Secret with Devices That Cannot Store Shares

Threshold cryptography increases security and resilience by sharing a private cryptographic key over different devices. Many personal devices, however, are not suited for threshold schemes, because they do not offer secure storage, which is needed to store shares of the private key. We present a solution that allows to include devices without them having to store their share. Shares are stored in protected form, possibly externally, which makes our solution suitable for low-cost devices with a factory-embedded key, e.g., car keys and access cards. By using pairings we achieve public verifiability in a wide range of protocols, which removes the need for private channels. We demonstrate how to modify existing discrete-log based threshold schemes to work in this setting. Our core result is a new publicly verifiable distributed key generation protocol that is provably secure against static adversaries and does not require all devices to be present.