Abstract: Various embodiments of the teachings herein include a method for arranging a shared cryptographic key with a communication partner. The method may include: selecting a first point of a first elliptic curve; sending the first point to the communication partner using a public channel; receiving a second point of the first elliptic curve from the communication partner; and determining the shared key using a non-trivial, inverse shared mapping of the second point with respect to a shared isomorphic mapping of a second elliptic curve onto the first elliptic curve.

Abstract: Various embodiments of the teachings herein include a method for arranging a shared cryptographic key with a communication partner. The method may include: selecting a first point of a first elliptic curve; sending the first point to the communication partner using a public channel; receiving a second point of the first elliptic curve from the communication partner; and determining the shared key using a non-trivial, inverse shared mapping of the second point with respect to a shared isomorphic mapping of a second elliptic curve onto the first elliptic curve.

Abstract: An automated system is provided. Examples of automated systems include processors for calculation which implement a secure boot process based on the plurality of numbers; chip cards for authentication; telecommunication equipment; programmable logic controllers, control devices for railways, etc. The operation is controlled depending on whether a sequential test for randomness of a plurality of numbers from a physical random number generator is marked as failed. This has the advantage that an online-test for integrity of the plurality of numbers is possible at a high accuracy and low latency.

Abstract: The invention relates to a method and an apparatus for designing a circuit suitable for generating random bits and to a circuit for generating random bits. A random bit string which is used as a binary random number is generated, for example. The proposed method and the apparatus as well as the circuit are used to implement random number generators, for example. A jth specific function from a set of bijective mappings is selected as the jth function, wherein the jth specific function carries out a jth fixed-point-free mapping. At least one ith mapping device is then selected. An ith specific function from a set of bijective mappings is assigned to the ith function, with the result that an ith concatenation of the i functions carries out an ith fixed-point-free mapping.

Abstract: The invention relates to a method and an apparatus for designing a circuit suitable for generating random bits and to a circuit for generating random bits. A random bit string which is used as a binary random number is generated, for example. The proposed method and the apparatus as well as the circuit are used to implement random number generators, for example. A jth specific function from a set of bijective mappings is selected as the jth function, wherein the jth specific function carries out a jth fixed-point-free mapping. At least one ith mapping device is then selected. An ith specific function from a set of bijective mappings is assigned to the ith function, with the result that an ith concatenation of the i functions carries out an ith fixed-point-free mapping.

Abstract: An apparatus for generating random bits includes a plurality of mapping devices. A respective mapping device is configured to map a predefined number of input signals, with the aid of a combinatorial mapping, into a predefined number of output signals. The plurality of mapping devices are concatenated with one another, and at least one combinatorial mapping is configured such that a state change of an input signal of a respective mapping device is mapped on average onto more than one output signal of the respective mapping device. No feedback loop is present such that a state change of at least one feedback output signal of a specific mapping device is fed as a state change of at least one input signal to another mapping device such that one or a plurality of output signals of the specific mapping device is influenced by the state change of the feedback output signal.

Abstract: An apparatus for generating random bits includes a plurality of mapping devices. A respective mapping device is configured to map a predefined number of input signals, with the aid of a combinatorial mapping, into a predefined number of output signals. The plurality of mapping devices are concatenated with one another, and at least one combinatorial mapping is configured such that a state change of an input signal of a respective mapping device is mapped on average onto more than one output signal of the respective mapping device. No feedback loop is present such that a state change of at least one feedback output signal of a specific mapping device is fed as a state change of at least one input signal to another mapping device such that one or a plurality of output signals of the specific mapping device is influenced by the state change of the feedback output signal.