1 Montgomery Modular Multiplication in Hard- ware

FEI KEMT
Cryptographic primitives belong to group of systems suitable for reconfigurable
devices due to the following features:
• standardized algorithms - most of the cryptographic algorithms, but random
number generators are approved by international standard organisations (e.g.
[54–56,58,59]). Thus, the functionality described by mathematical algorithms
and equations can by deeply studied and tailored to the hardware structure. It
is possible that group of secure cryptographic algorithms is changed in the time
due to newly invented attacks. The reconfigurable platform makes possible to
remove obsolete algorithms from running systems and provide the new ones,
even without hardware update or exchange.
• several supported functionality modes and lengths of operands - while the num-
ber of the most popular algorithms is limited, each of them provides a group of
selectable parameters what results in need to implement a group of algorithms
combinations.
• sequential structure - in dependency on running operation only selected crypto-
graphic blocks need to programmed in a device and in case of operation change
the other configuration is loaded. As an example we mentioned a scheme when
at the beginning of the communication a secret key is distributed to the parties
by an asymmetric algorithm which is later misplaced by a faster symmetric
encryption implemented on the same device.
FPGA Architecture The underlying FPGA architecture consists of an array of
the smallest programmable units - logic elements (LE) or configurable logic blocks
(CLB), and the programmable connection switches. A typical FPGA architecture
consists of a high number (hundreds to thousands) of LEs and routing channels with
different length/speed. By the LE we understand the smallest functional unit that
is addressed by the mapping tools. Typically it consists of a look-up table (LUT)
and a register (D flip-flop) (see Figure 1 – 1), what makes possible to implement the
combinatorial as well as sequential logic, or a small memory block. Additionally, the
FPGA architecture may include special dedicated blocks or building items for other
functions e.g. for storing data, computing multiplication and addition, synthesis
clock signals. . .
Modern FPGAs provide support for implementation of a wide range of the algo-
rithms from area of signal processing, communication or networking. The crypto-
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