Cryptography Reference
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Figure 9.6. The Improved Hybrid Implementation
It is also sometimes helpful if a register fixed with the constant value of zero is avail-
able. The processor must support simple indexed memory load and store instructions,
an integer multiply instruction that outputs the result in a pair of registers, and a simple
add-with-carry instruction. The implementation of the improved hybrid method is
always processor specific, as CPUs differ in small but significant ways that cannot be
described in a one-size-fits-all way.
9.8.2 Effi cient Binary Field Arithmetic for Low-End Processors
Finite fields of characteristic-two are usually the main alternative to prime fields
when implementing ECC systems. Binary fields are attractive, especially for hardware
implementations, since the operations in F 2 m involve only shifts and bitwise addition
modulo 2. The simplicity of basic operations is also attractive for software implementa-
tions on general-purpose processors. Prime and binary fields have their own pros and
cons when it comes to efficient implementation on low-end processors. The most time-
critical operation in F 2 m is binary polynomial multiplication, which involves calcu-
lations of a few bits at a time and can be very slow without proper optimizations. On
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