Leading certificate authority Let’s Encrypt is facing criticism that its rapid growth and eagerness to encrypt internet communications is happening at a cost.

Researchers at SEC Consult say the number of internet gateways, routers, modems and other embedded devices sharing cryptographic keys and certificates is up 40 percent since the Austrian consulting firm first looked at the problem in November. The report, posted Tuesday called “House of Keys,” warns a sharp rise of devices using known private keys...