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Bluetooth (BR/EDR) and Bluetooth Low Energy (BLE) are pervasive wireless technologies specified in the Bluetooth standard. The standard includes key negotiation protocols used to generate long-term keys (during pairing) and session keys (during secure connection establishment). In this work, we demonstrate that the key negotiation protocols of Bluetooth and BLE are vulnerable to standard-compliant entropy downgrade attacks. In particular, we show how an attacker can downgrade the entropy of any Bluetooth session key to 1 byte, and of any BLE long-term key and session key to 7 bytes. Such low entropy values enable the attacker to brute-force Bluetooth long-term keys and BLE long-term and session keys, and to break all the security guarantees promised by Bluetooth and BLE. As a result of our attacks, an attacker can decrypt all the ciphertext and inject valid ciphertext in any Bluetooth and BLE network.