Quantifying Shannon's Work Function for Cryptanalytic Attacks

Attacks on cryptographic systems are limited by the available computational resources. A theoretical understanding of these resource limitations is needed to evaluate the security of cryptographic primitives and procedures. This study uses an Attacker versus Environment game formalism based on computability logic to quantify Shannon's work function and evaluate resource use in cryptanalysis. A simple cost function is defined which allows to quantify a wide range of theoretical and real computational resources. With this approach the use of custom hardware, e.g., FPGA boards, in cryptanalysis can be analyzed. Applied to real cryptanalytic problems, it raises, for instance, the expectation that the computer time needed to break some simple 90 bit strong cryptographic primitives might theoretically be less than two years.Comment: 19 page

A framework for FPGA functional units in high performance computing

FPGAs make it practical to speed up a program by defining hardware functional units that perform calculations faster than can be achieved in software. Specialised digital circuits avoid the overhead of executing sequences of instructions, and they make available the massive parallelism of the components. The FPGA operates as a coprocessor controlled by a conventional computer. An application that combines software with hardware in this way needs an interface between a communications port to the processor and the signals connected to the functional units. We present a framework that supports the design of such systems. The framework consists of a generic controller circuit defined in VHDL that can be configured by the user according to the needs of the functional units and the I/O channel. The controller contains a register file and a pipelined programmable register transfer machine, and it supports the design of both stateless and stateful functional units. Two examples are described: the implementation of a set of basic stateless arithmetic functional units, and the implementation of a stateful algorithm that exploits circuit parallelism