1 Montgomery Modular Multiplication in Hard- ware

Preface
Systems for public key cryptography are intensively applied in order to digitally sign
or encrypt data. In this way we assure integrity and confidentiality of the signed
message and provide authentication and non-repudiation features for a signer. The
complexity of computations has impact on performance of the system, especially in
case of long keys. The security of the operations is based on secrecy of the private
key, while its public part and the algorithm itself are publicly known.
In the first part of thesis we analyse the computational part of the systems and
focus on flexible implementation of modular multiplier. The output of the research
was applied in order to estimate performance of Elliptic Curve Method (ECM)
increased thanks to its hardware realisation. Scalable nature of the multiplier was
spread in the whole design, and the proof-of-concept implementation was designed
and tested in a very short time.
In the second part of document we focus on the key generating element – a Ran-
dom Number Generator (RNG). Already known design was analysed under several
aspects and we provide results in the form of a stochastic model of the RNG and
proposed testing methods suitable for this type of RNGs.
The target platform for the selected building blocks of cryptosystems is FPGA
(Field Programmable Gate Array) what offers a reduction of development time, wide
range of devices and high level of security. In the thesis analyse particular families of
devices from FPGA vendors which include dedicated electronic elements used in our
designs. Parameters of the blocks and algorithm improvements may have significant
impact on the performance of system.
Three topics of the thesis provide a picture of complexity level in cryptology and
underline relevance of research in area of cryptographic systems implementation.