A new multiplier that supports fields GF(p) and GF (2n) for the public-key cryptography, and fields GF (28) for the secret-key cryptography is proposed in this thesis. Based on the core multiplier and other extracted common operations, a novel hybrid crypto-processor is built which processes both public-key and secret-key cryptosystems. The corresponding instruction set is also presented. Three cryptographic algorithms: the Elliptic Curve Cryptography (ECC), AES and RC5 are focused to run in the processor. To compute scalar multiplication kP efficiently, a blend of efficient algorthms on elliptic curves and coordinates selections and of hardware architecture that supports arithmetic operations on finite fields is requried. The Nonadjacent Form (NAF) of k is used in Jacobian projective coordinates over GF(p); Montgomery scalar multiplication is utilized in projective coordinates over GF(2n). The dual-field multiplier is used to support multiplications over GF(p) and GF(2n) according to multiple-precision Montgomery multiplications algorithms. The design ideas of AES and RC5 are also described. The proposed hybrid crypto-processor increases the flexibility of security schemes and reduces the total cost of cryptosystems. / viii, 87 leaves : ill. (some col.) ; 28 cm.