Intellectual Property

Method and Apparatus of Calculating a Modular Inverse

Method and Apparatus of Calculating a Modular Inverse

Researchers at QUB have invented A novel hardware architecture for elliptic curve cryptography (ECC) over GF(p)



ELLIPTIC curve cryptosystems (ECCs) are increasingly becoming a more attractive alternative to traditional RSA systems, as these offer similar security but for a much smaller key size. For instance, a 256-bit ECC key size provides the same level of security as an equivalent 3072-bit RSA key. This key size gap is set to further increase in future systems when security requirements become more demanding. Therefore, smaller finite field arithmetic is required to encrypt data by using ECCs, allowing potentially higher data rates at a much lower implementation cost.


This new hardware ECC processor architecture can perform the main prime field arithmetic functions needed in these cryptosystems and in particular comprises modular inversion and multiplication components. It uses a combination of a new unified inversion algorithm and novel full-word multiplier architectures, which display impressive throughput rates when implemented efficiently in hardware.

This is based on a new unified modular inversion algorithm that offers considerable improvement over previous ECC techniques that use Fermat’s little Theorem for this operation


Ciaran McIvor

Patent Status

This work is the subject of patent application. A provisional patent application was filed on 24May 2004. The patent was granted in Europe on 2 Dec 2009.

Application number: 11/139,957


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