The ever-increasing need for securing computing systems using cryptographic algorithms is spurring interest in the efficient implementation of common algorithms. While the algorithms can be implemented in software using base instruction sets, there is considerable potential to reduce memory cost and improve speed using specialized instructions and associated hardware. However, there is a need to assess the benefits and costs of software implementations and new instructions that implement key cryptographic algorithms in fewer cycles. The primary aim of this paper is to improve the understanding of the performance and cost of implementing cryptographic algorithms for the RISC-V instruction set architecture (ISA) in two cases: software implementations of the algorithms using the rv32i instruction set and using cryptographic instructions supported by dedicated hardware in additional functional units. For both cases, we describe a RISC-V processor with cryptography hardware extensions and hand-optimized RISC-V assembly language implementations of eleven cryptographic algorithms. Compared to implementations with only the rv32i instruction set, implementations with the cryptography set extension provide a 1.5× to 8.6× faster execution speed and 1.2× to 5.8× less program memory for five of the eleven algorithms. Based on our performance analyses, a new instruction is proposed to increase the implementation efficiency of the algorithms.