Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The article describes a novel class of arithmetic architectures for Galois fields GF(2/sup k/). The main applications of the architecture are public key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF(2/sup k/) as GF((2/sup n/)/sup m/), where k=n/spl middot/m. The approach explores bit parallel arithmetic in the subfield GF(2/sup n/) and serial processing for the extension field arithmetic. This mixed parallel-serial (hybrid) approach can lead to fast implementations. As the core module, a hybrid multiplier is introduced and several optimizations are discussed.  provide two different approaches to squaring.  develop exact expressions for the complexity of parallel squarers in composite fields, which can have a surprisingly low complexity. The hybrid architectures are capable of exploring the time-space trade-off paradigm in a flexible manner. In particular, the number of clock cycles for one field multiplication, which is the atomic operation in most public key schemes, can be reduced by a factor of n compared to other known realizations. The acceleration is achieved at the cost of an increased computational complexity.  describe a proof-of-concept implementation of an ASIC for multiplication and squaring in GF((2/sup n/)/sup m/), m variable.
['Christof Paar', 'Peter Fleischmann', 'Pedro Soria-Rodriguez']
I am writing a research paper on a idea Fast arithmetic for public-key algorithms in Galois fields with composite exponents
[{"from": "human", "value": "I am writing a research paper on a idea Fast arithmetic for public-key algorithms in Galois fields with composite exponents"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The article describes a novel class of arithmetic architectures for Galois fields GF(2/sup k/). The main applications of the architecture are public key systems which are based on the discrete logarithm problem for elliptic curves. The architectures use a representation of the field GF(2/sup k/) as GF((2/sup n/)/sup m/), where k=n/spl middot/m. The approach explores bit parallel arithmetic in the subfield GF(2/sup n/) and serial processing for the extension field arithmetic. This mixed parallel-serial (hybrid) approach can lead to fast implementations. As the core module, a hybrid multiplier is introduced and several optimizations are discussed.  provide two different approaches to squaring.  develop exact expressions for the complexity of parallel squarers in composite fields, which can have a surprisingly low complexity. The hybrid architectures are capable of exploring the time-space trade-off paradigm in a flexible manner. In particular, the number of clock cycles for one field multiplication, which is the atomic operation in most public key schemes, can be reduced by a factor of n compared to other known realizations. The acceleration is achieved at the cost of an increased computational complexity.  describe a proof-of-concept implementation of an ASIC for multiplication and squaring in GF((2/sup n/)/sup m/), m variable."}]