Clifford Christopher Cocks (born 28 December 1950) is a British mathematician and

cryptographer Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More gen ...

. In the early 1970s, while working at the United Kingdom

Government Communications Headquarters Government Communications Headquarters (GCHQ) is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the United Kingdom. Primari ...

(GCHQ), he developed an early

public-key cryptography Public-key cryptography, or asymmetric cryptography, is the field of cryptographic systems that use pairs of related keys. Each key pair consists of a public key and a corresponding private key. Key pairs are generated with cryptographic alg ...

(PKC) system. This pre-dated commercial offerings, but due to the classified nature of Cocks' work, it did not become widely known until 1997 when the work was declassified. As his work was not available for public review until 1997, it had no impact on numerous commercial initiatives relating to Internet security that had been commercially developed and that were well established by 1997. His work was technically aligned with the

Diffie–Hellman key exchange Diffie–Hellman (DH) key exchangeSynonyms of Diffie–Hellman key exchange include: * Diffie–Hellman–Merkle key exchange * Diffie–Hellman key agreement * Diffie–Hellman key establishment * Diffie–Hellman key negotiation * Exponential ke ...

and elements of the

RSA algorithm The RSA (Rivest–Shamir–Adleman) cryptosystem is a public-key cryptography, public-key cryptosystem, one of the oldest widely used for secure data transmission. The initialism "RSA" comes from the surnames of Ron Rivest, Adi Shamir and Leonar ...

; these systems were independently developed and commercialized.

Education

Cocks was educated at

Manchester Grammar School The Manchester Grammar School (MGS) is a highly Selective school, selective Private_schools_in_the_United_Kingdom, private day school for boys aged 7-18 in Manchester, England, which was founded in 1515 by Hugh Oldham (then Bishop of Exeter). ...

and went on to study the

Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics, University of Cambridge, Faculty of Mathematics at the University of Cambridge. Origin In its classical nineteenth-century form, the tripos was a di ...

as an undergraduate at

King's College, Cambridge King's College, formally The King's College of Our Lady and Saint Nicholas in Cambridge, is a List of colleges of the University of Cambridge, constituent college of the University of Cambridge. The college lies beside the River Cam and faces ...

. He continued as a PhD student at the

University of Oxford The University of Oxford is a collegiate university, collegiate research university in Oxford, England. There is evidence of teaching as early as 1096, making it the oldest university in the English-speaking world and the List of oldest un ...

, where he specialised in

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

under Bryan Birch, but left academia without finishing his doctorate.In conversation with Clifford Cocks
/ref>

Career

Non-secret encryption

Cocks left Oxford to join Communications-Electronics Security Group (CESG), an arm of GCHQ, in September 1973. Soon after, Nick Patterson told Cocks about James H. Ellis' ''non-secret encryption,'' an idea which had been published in 1969 but never successfully implemented. Several people had attempted creating the required

one-way function In computer science, a one-way function is a function that is easy to compute on every input, but hard to invert given the image of a random input. Here, "easy" and "hard" are to be understood in the sense of computational complexity theory, s ...

s, but Cocks, with his background in number theory, decided to use

prime factorization In mathematics, integer factorization is the decomposition of a positive integer into a product of integers. Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a comp ...

, and did not even write it down at the time. With this insight, he quickly developed what later became known as the RSA encryption algorithm. GCHQ was not able to find a way to use the algorithm, and treated it as

classified information Classified information is confidential material that a government deems to be sensitive information which must be protected from unauthorized disclosure that requires special handling and dissemination controls. Access is restricted by law or ...

. The scheme was also passed to the NSA. With a military focus, financial considerations, and low computing power, the power of public-key cryptography was unrealised in both organisations:

I judged it most important for military use. In a fluid military situation you may meet unforeseen threats or opportunities. ... if you can share your key rapidly and electronically, you have a major advantage over your opponent. Only at the end of the evolution from Berners-Lee n 1989designing an open internet architecture for CERN, its adaptation and adoption for the Arpanet ... did public key cryptography realise its full potential. - Ralph BenjaminGCHQ pioneers on birth of public-key crypto
/ref>

In 1977, the algorithm was independently invented and published by Rivest, Shamir and Adleman, who named it after their initials. There is no evidence of a hint or leak, conscious or unconscious, and Cocks has dismissed the idea. The British achievement remained secret until 1997.

Public revelation

In 1987, the GCHQ had plans to release the work, but Peter Wright's '' Spycatcher'' MI5 memoir caused them to delay revealing the research by ten years. 24 years after its discovery, on 18 December 1997, Cocks revealed the GCHQ history of public-key research in a public talk. James Ellis had died on 25 November 1997, a month before the public announcement was made.

Identity-based encryption

In 2001, Cocks developed one of the first secure identity-based encryption (IBE) schemes, based on assumptions about

quadratic residues In number theory, an integer ''q'' is a quadratic residue modulo ''n'' if it is congruent to a perfect square modulo ''n''; that is, if there exists an integer ''x'' such that :x^2\equiv q \pmod. Otherwise, ''q'' is a quadratic nonresidue mod ...

in composite groups. The Cocks IBE scheme is not widely used in practice due to its high degree of

ciphertext expansion In cryptography, the term ciphertext expansion refers to the length increase of a message when it is encrypted. Many modern cryptosystems cause some degree of expansion during the encryption process, for instance when the resulting ciphertext must ...

. However, it is currently one of the few IBE schemes which do not use bilinear pairings, and rely for security on more well-studied mathematical problems.

Awards and honours

In 1968, Cocks won a silver medal at the 10th

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is widely regarded as the most prestigious mathematical competition in the wor ...

. Cocks held the post of Chief Mathematician at GCHQ. He established the Heilbronn Institute for Mathematical Research at the

University of Bristol The University of Bristol is a public university, public research university in Bristol, England. It received its royal charter in 1909, although it can trace its roots to a Merchant Venturers' school founded in 1595 and University College, Br ...

. Cocks was made a Companion of the

Order of the Bath The Most Honourable Order of the Bath is a British order of chivalry founded by King George I of Great Britain, George I on 18 May 1725. Recipients of the Order are usually senior British Armed Forces, military officers or senior Civil Service ...

in 2008 (the citation describes him as "Counsellor, Foreign and Commonwealth Office"). He was awarded an honorary degree from the

in 2008, and an honorary Doctor of Science from the

University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...

in 2015. With James Ellis and Malcolm Williamson, Cocks was honoured for his part in the development of public-key cryptography by the

Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE has a corporate office ...

(IEEE) in 2010 and by induction into the Cryptologic Hall of Honor in 2021. Cocks was elected a Fellow of the Royal Society (FRS) in 2015. His certificate of election reads:

References

{{DEFAULTSORT:Cocks, Clifford 1950 births Living people People educated at Manchester Grammar School Alumni of King's College, Cambridge GCHQ cryptographers Public-key cryptographers Fellows of the Royal Society Companions of the Order of the Bath International Mathematical Olympiad participants