Abstract: In some embodiments, apparatuses and methods are provided herein useful to monitor athletic performance. In some embodiments, one or more control circuits and sensors are used to analyze performance as it compares to music tempo that is played during an exercise session or class, which may be done both directly and/or indirectly. In one embodiment, athletic performance during an exercise period is monitored and compared to the tempos of music played, where the music tempo is identified by one of measuring the actual tempo of the music played and/or obtaining the tempo from a database or otherwise associating the selection(s) played with an identified tempo of the music itself. In another embodiment, the music tempo is indirectly identified or analyzed, such as by analyzing the performance or cadence of a group of exercisers and comparing the performance parameters sensed to obtain a benchmark tempo from which to compare individual users.

Abstract: In some embodiments, apparatuses and methods are provided herein useful to monitor athletic performance. In some embodiments, one or more control circuits and sensors are used to analyze performance as it compares to music tempo that is played during an exercise session or class, which may be done both directly and/or indirectly. In one embodiment, athletic performance during an exercise period is monitored and compared to the tempos of music played, where the music tempo is identified by one of measuring the actual tempo of the music played and/or obtaining the tempo from a database or otherwise associating the selection(s) played with an identified tempo of the music itself. In another embodiment, the music tempo is indirectly identified or analyzed, such as by analyzing the performance or cadence of a group of exercisers and comparing the performance parameters sensed to obtain a benchmark tempo from which to compare individual users.

Abstract: In some embodiments, apparatuses and methods are provided herein useful to monitor athletic performance. In some embodiments, one or more control circuits and sensors are used to analyze performance as it compares to music tempo that is played during an exercise session or class, which may be done both directly and/or indirectly. In one embodiment, athletic performance during an exercise period is monitored and compared to the tempos of music played, where the music tempo is identified by one of measuring the actual tempo of the music played and/or obtaining the tempo from a database or otherwise associating the selection(s) played with an identified tempo of the music itself. In another embodiment, the music tempo is indirectly identified or analyzed, such as by analyzing the performance or cadence of a group of exercisers and comparing the performance parameters sensed to obtain a benchmark tempo from which to compare individual users.

Abstract: A method for delegating a computational burden from a computationally limited party to a computationally superior party is disclosed. Computations that can be delegated include inversion and exponentiation modulo any number m. This can be then used for sending encrypted messages by a computationally limited party in a standard cryptographic framework, such as RSA. Security of delegating computation is not based on any computational hardness assumptions, but instead on the presence of numerous decoys of the actual secrets.

Abstract: A method for delegating a computational burden from a computationally limited party to a computationally superior party is disclosed. Computations that can be delegated include inversion and exponentiation modulo any number m. This can be then used for sending encrypted messages by a computationally limited party in a standard cryptographic framework, such as RSA. Security of delegating computation is not based on any computational hardness assumptions, but instead on the presence of numerous decoys of the actual secrets.