A High-Speed FPGA Implementation of an RSD-Based ECC Processor


In this paper, an exportable application-specific instruction-set elliptic curve cryptography processor based on redundant signed digit representation is proposed. The processor employs extensive pipelining techniques for Karatsuba–Ofman method to achieve high throughput multiplication. Furthermore, an efficient modular adder without comparison and a high throughput modular divider, which results in a short datapath for maximized frequency, are implemented. The proposed architecture of this paper analysis the logic size, area and power consumption using Xilinx 14.2.

Enhancement of the project:

Existing System:

In prime field ECC processors, carry free arithmetic is necessary to avoid lengthy datapaths caused by carry propagation. Redundant schemes, such as carry save arithmetic (CSA), redundant signed digits (RSDs) , or residue number systems (RNSs) , have been utilized in various designs. Carry logic or embedded digital signal processing (DSP) blocks within fieldprogrammable gate arrays (FPGAs) are also utilized in some designs to address the carry propagation problem. It is necessary to build an efficient addition data path since it is a fundamental operation employed in other modular arithmetic operations. Modular multiplication is an essential operation in ECC.

Two main approaches may be employed. The first is known as interleaved modular multiplication using Montgomery’s method. Montgomery multiplication is widely used in implementations where arbitrary curves are desired. Another approach is known as multiply-then-reduce and is used in elliptic curves built over finite fields of Merssene primes. Merssene primes are the special type of primes which allow for efficient modular reduction through series of additions and subtractions. In order to optimize the multiplication process, some ECC processors use the divide and conquer approach of Karatsuba–Ofman multiplications, where others use embedded multipliers and DSP blocks within FPGA fabrics.


  • long data paths
  • less frequency range