System for securely transmitting data, having a) a control device, which is designed to use a physically unclonable function, PUF, to produce a cryptographic key; and b) having at least one security module, coupled to the control device, which is designed to communicate with the control device confidentially and/or authentically on the basis of the cryptographic key produced; c) wherein the control device does not have an access-protected nonvolatile memory for storing the cryptographic key, and d1) wherein the security module has an access-protected nonvolatile memory and a computation device, which is designed to receive the cryptographic key produced from the control device and to store it in the nonvolatile memory; and d2) wherein the security module, after transmitting the key, is locked against renewed transmission of the cryptographic key; e) wherein the security module is designed to receive the cryptographic key from the control device only a single time and to store the received cryptographic key in the access-protected nonvolatile memory, wherein the access-protected nonvolatile memory is in the form of a write-once memory; and/or wherein the control device is designed to provide the cryptographic key for the security module only a single time; and f1) wherein the control device and the security module each have a communication interface (12; 13) and are designed to use the communication interfaces (12, 13) to interchange data; f2) wherein the control device is designed to first of all provide the security module with the cryptographic key via the communication interfaces (12, 13) in an unencrypted data transmission and, following the data transmission of the cryptographic key, to communicate with the security module in encrypted form and/or authentically on the basis of the transmitted cryptographic key; and f3) wherein the security module is designed to use the communication interfaces (12, 13) to first of all communicate with the control device in unencrypted form and, following the receipt of the cryptographic key, to communicate with the control device in encrypted form and/or authentically on the basis of the received cryptographic key. a) a control device, which is designed to use a physically unclonable function, PUF, to produce a cryptographic key; and b) having at least one security module, coupled to the control device, which is designed to communicate with the control device confidentially and/or authentically on the basis of the cryptographic key produced; c) wherein the control device does not have an access-protected nonvolatile memory for storing the cryptographic key, and d1) wherein the security module has an access-protected nonvolatile memory and a computation device, which is designed to receive the cryptographic key produced from the control device and to store it in the nonvolatile memory; and d2) wherein the security module, after transmitting the key, is locked against renewed transmission of the cryptographic key; e) wherein the security module is designed to receive the cryptographic key from the control device only a single time and to store the received cryptographic key in the access-protected nonvolatile memory, wherein the access-protected nonvolatile memory is in the form of a write-once memory; and/or wherein the control device is designed to provide the cryptographic key for the security module only a single time; and f1) wherein the control device and the security module each have a communication interface (12; 13) and are designed to use the communication interfaces (12, 13) to interchange data; f2) wherein the control device is designed to first of all provide the security module with the cryptographic key via the communication interfaces (12, 13) in an unencrypted data transmission and, following the data transmission of the cryptographic key, to communicate with the security module in encrypted form and/or authentically on the basis of the transmitted cryptographic key; and f3) wherein the security module is designed to use the communication interfaces (12, 13) to first of all communicate with the control device in unencrypted form and, following the receipt of the cryptographic key, to communicate with the control device in encrypted form and/or authentically on the basis of the received cryptographic key.