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An architecture includes a controller. The controller is configured to receive a microprogram. The microprogram is configured for performing at least one of hierarchical or a sequence of polynomial computations. The architecture also includes an arithmetic logic unit (ALU) communicably coupled to the controller. The ALU is controlled by the controller. Additionally, the microprogram is compiled prior to execution by the controller, the microprogram is compiled into a plurality of binary tables, and the microprogram is programmed in a command language in which each command includes a first portion for indicating at least one of a command or data transferred to the ALU, and a second portion for including a control command to the controller. The architecture and implementation of the programmable controller may be for cryptographic applications, including those related to public key cryptography.