Cryptography has a key role to provide security for data communication over the fast growing computer networks. This thesis describes high performance techniques which speed up the modular exponentiation based public-key cryptography algorithms. A new algorithm based on the Montgomery reduction method, called the M4 algorithm, is proposed for modular multiplication. This algorithm, which decreases the modulus size in the operation, increases the performance of the modular operation by calculating the quotient after the partial result computation. The second novel algorithm proposed in this thesis performs modular reduction in a similar manner as the modified Booth approach in multiplication. A simplification in the quotient calculation for the modular multiplication in the radix 4 is also introduced. These efficient techniques can double the speed of the modular multiplication at little cost. A CryptoProcessor has been designed as a single chip implementation for the RSA algorithm which is one of the most reliable complete public-key cryptosystems available today. This processor is capable of executing 512-bit modular exponentiation, so it can be used for other algorithms such as the Diffie-Hellman key exchange scheme and the El-Gamal digital signature algorithm. Using 0.7mu CMOS technology and a single-bit scan technique, the CryptoProcessor has achieved 62 kbps modular exponentiation rate in 50 MHz clock frequency without employing the Chinese remainder theorem (CRT). The two other features of the CryptoProcessor are as follows: (1) keys of arbitrary size (up to 512-bit) can be used; (2) the architecture of the CryptoProcessor is capable of handling various methods of exponentiation. Furthermore using techniques described in this thesis, it is shown how the CryptoProcessor can achieve speeds up to 4.4 Mbps. Algorithms which provide pipelining techniques in the high radix implementations are also introduced. In addition to overcoming the delay caused by pipelining, a novel algorithm pipelines the quotient calculation in algorithmic level resulting in a single-digit quotient for each iteration. Other algorithms result in non-single digit quotients. Another novel algorithm avoids the result size increase which is another drawback in the quotient pipelining. Combining both techniques yields an algorithm which removes these two main problems from the quotient pipelining. A precise description of the behaviour of these algorithms is presented. The MATHIC package as a portable and easy-to-use package has been developed to support multiprecision operations. The package was written in C++ and is useful to verify and to debug the large integer algorithms which are implemented in hardware. A new type of variable has been introduced as 'BitVector' which combines the bit-vector type and the multiprecision integer type with an arbitrary size.