
Patenting mathematics-based inventions: Navigating sufficiency and the inventive step squeeze
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Terence Broderick

Remember face-to-face business meetings, where you could make agreements in the physical world and sign by hand on the dotted line? During the past year, when all such meetings were shunted into the virtual realm, we have become increasingly reliant on digital signatures. If you’re innovating to improve digital signatures, or working on any type of cryptographic inventions, this one’s for you — your invention could benefit from IP protection to help you commercialise.
To understand how to protect aspects of a digital signature, we must first spell out exactly what one is. While the concept of an electronic signature has been around for a long time, a digital signature is considered to be more sophisticated and supported by cryptographical techniques.
In principle, a digital signature associates the content of a document with a public-private key pair, generated using public key infrastructure (PKI) techniques. It typically applies principles of abstract algebra (a branch of mathematics that covers the key concepts of groups, rings and fields) to generate signatures that are very difficult to infiltrate.
Digital signatures are thought to have been initially developed in the early 1970s at Government Communication Headquarters (GCHQ) in the UK. They have been used for many years to sign documents where the authenticity of the content is key. Patent applications would be one example of such a document.
Digital signatures are also frequently used in situations where it is important to detect forgery or tampering. They are commonly used during the distribution of software and the approval of financial transactions.
With digital signatures having become a staple of everyday life, they’re set to grow in importance even after we return to normality post-lockdown.
The increasing use of over-the-air technology when delivering software updates to vehicles is a huge potential growth area for digital signatures, which could provide the necessary security without interrupting the use of the vehicle. Essentially, the vehicle and the software provider would have their own digital signatures that can be provided by the vehicle automatically, without (at least for certain applications) requiring driver input.
The proliferation of the Internet-of-Things (IoT) is another area that is set to see considerable development in this space. Devices could each have their own digital signatures, enabling them to sign their own messages when communicating with other devices on the IoT.
However, digital signatures are not perfect and, in the age of ever more powerful computers and knowledge about cryptographic concepts, vulnerabilities are inherent and can be exploited. Each application of digital signatures will no doubt throw up their own challenges but there are some challenges which will no doubt be common to all applications:
These typically reside in:
The increased focus on the use of digital signatures during the COVID-19 pandemic is sure to have identified a raft of problems — and, naturally, solutions are sure to have been developed.
For example, you may have identified an application of mathematics that makes the digital signature more difficult to infiltrate, or developed decryption software to highlight the likelihood of a malicious actor having obtained private keys used to sign the document (thereby introducing the question of an attack on its content).
Even though this may involve the application of mathematics or another abstract concept, if the application of mathematics addresses a technical problem then it may well be patentable.
Our software team has substantial experience with cryptography- and mathematics-focused inventions.
If you’re developing improvements to digital signatures, get in touch with us to discuss your invention in a confidential environment, where we can use our experience and expertise to advise on how you should protect your invention.
Meet the author

About Terence Broderick

Murgitroyd is a leading intellectual property firm supporting innovative businesses across a wide range of sectors. From patents and trade marks to designs, copyright, and IP strategy, their expertise extends beyond legal protection to helping organisations maximise the value of their ideas. Working across industries such as life sciences, engineering, technology, and creative sectors, Murgitroyd combines technical insight with commercial understanding to deliver tailored, forward-thinking solutions.