In one embodiment, an apparatus includes a hardware accelerator to execute cryptography operations including a Rivest Shamir Adleman (RSA) operation and an elliptic curve cryptography (ECC) operation. The hardware accelerator may include a multiplier circuit comprising a parallel combinatorial multiplier, and an ECC circuit coupled to the multiplier circuit to execute the ECC operation. The ECC circuit may compute a prime field multiplication using the multiplier circuit and reduce a result of the prime field multiplication in a plurality of addition and subtraction operations for a first type of prime modulus. The hardware accelerator may execute the RSA operation using the multiplier circuit. Other embodiments are described and claimed.