Modern cryptography is undoubtedly one of the most mathematically intensive fields of applied computer science. The advent of public key cryptography has opened the field to advanced branches of pure mathematics, such as Algebraic Geometry, where objects known as Elliptic curves are studied. Elliptic Curve Cryptography (ECC) has been the foundation of some of the most exciting emerging technologies over the past ten years, including Blockchain.
We offer comprehensive mathematical support services for designing, evaluating and implementing cutting-edge modern cryptographic schemes:
Elliptic & Hyperelliptic Curve Cryptography: The discrete logarithm problem (DLP) cryptosystem based on elliptic and hyperelliptic curves is far more efficient to implement than prime factoring problem cryptosystems such as RSA due to smaller key sizes that elliptic and hyperelliptic curves enable for the same level of security as large size key RSA. However, while elliptic curves are widely used in popular modern protocols such as the Elliptic Curve Digital Signature Algorithm (ECDSA), their cousins' hyperelliptic curves have yet to find wide practical adoption. This is partly due to mathematical barriers encountered on the implementation side, i.e. hyperelliptic curves are mathematically more subtle and so harder for applied cryptographers to handle.
Post-Quantum Cryptography (PQC): It's a fact that when we finally have quantum computers capable of executing the likes of Shor's algorithms that can solve both the factoring and discrete logarithm problem, then RSA, ECC and many other fundamental cryptographic primitives will become completely obsolete! This means organisations with long-shelf life-sensitive information need to consider Post-Quantum Cryptography as a secure alternative as soon as possible to avoid threats such as Harvest-Now Decrypt Later. Indeed, NIST recently published the first four standards for PQC (see here). Some of the most promising candidates for PQC are Lattice cryptography, Multivariate cryptography and Code-based cryptography.
Multiparty-Computation (MPC): MPC has found some new exciting applications, such as Federated Machine Learning, where multiple parties collaborate to train a standard machine learning model whilst not giving up access to sensitive data. It is one of the most popular Privacy-Preserving Technologies (PETS) implementation approaches.
Fully Homomorphic Encryption (FHE): Traditionally, Encryption has been, of course, the security solution of choice for protecting data. However, Encryption is impractical for data analytics and data mining, which cannot be effective without decrypting the data first, thereby re-introducing vulnerability. Data anonymisation may be used to provide security and confidentiality during data mining operations and performs well with tabular data. However, it is much less efficient with free text data, where processes like automatic identification of anonymised words, such as proper nouns, are only guaranteed effective in some cases. Fully Homomorphic encryption (FHE) is, in a nutshell, a cryptographic scheme that allows arbitrary computation to be applied directly to cipher text without any decryption beforehand, during or after the computation. The result of the computation, once decryption has been applied, should be the same as if it was applied to unencrypted data. Hence, FHE could allow organisations to be far more open to sharing sensitive data with trusted third parties for collaboration and innovation purposes without compromising the integrity and security of the data.
Firstly, we deeply understand the enormous pressure enterprise organisations face to evolve and embrace next-generation technology in an ever-growing competitive global digital market where access to sensitive data is important. The key outcome of our Cryptography consulting service is to help data-driven enterprise organisations build the mathematical capabilities that redefine their business models to stay relevant, compete, and be leaders in their core markets. Secondly, our consulting team comprises the brightest young PhD-level mathematicians who complete our tailored academia-to-industry transition program with an emphasis on Cryptography. Here are some of the benefits of working with us:
Our team is ready to help your organisation transform its operations at the intersection of frontier Cryptography research innovation and customer needs. Would you like to learn how we can unlock your in-house technical talent superpowers with our collaboration while preserving your independence?
Get in touch with our team today!