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

cryptographer Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...

. In 1973, while working at the United Kingdom

Government Communications Headquarters Government Communications Headquarters, commonly known as 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 Uni ...

(GCHQ), he invented a

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 a ...

algorithm equivalent to what would become (in 1977) the RSA algorithm. The idea was

classified information Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to kn ...

and his insight remained hidden for 24 years, although it was independently invented by

Ronald Rivest Ronald Linn Rivest (; born May 6, 1947) is a cryptographer and an Institute Professor at MIT. He is a member of MIT's Department of Electrical Engineering and Computer Science (EECS) and a member of MIT's Computer Science and Artificial Int ...

Adi Shamir Adi Shamir ( he, עדי שמיר; born July 6, 1952) is an Israeli cryptographer. He is a co-inventor of the Rivest–Shamir–Adleman (RSA) algorithm (along with Ron Rivest and Len Adleman), a co-inventor of the Feige–Fiat–Shamir identifi ...

, and

Leonard Adleman Leonard Adleman (born December 31, 1945) is an American computer scientist. He is one of the creators of the RSA encryption algorithm, for which he received the 2002 Turing Award, often called the Nobel prize of Computer science. He is also kno ...

in 1977. Public-key cryptography using prime factorisation is now part of nearly every Internet transaction.

Education

Cocks was educated at

Manchester Grammar School The Manchester Grammar School (MGS) in Manchester, England, is the largest independent school (UK), independent day school for boys in the United Kingdom. Founded in 1515 as a Grammar school#free tuition, free grammar school next to Manchester C ...

and went on to study the

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

as an undergraduate at

King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the cit ...

. He continued as a PhD student at the

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

, where he specialised in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Ma ...

under

Bryan Birch Bryan John Birch FRS (born 25 September 1931) is a British mathematician. His name has been given to the Birch and Swinnerton-Dyer conjecture. Biography Bryan John Birch was born in Burton-on-Trent, the son of Arthur Jack and Mary Edith 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 Government Communications Headquarters, commonly known as 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 Unit ...

(CESG), an arm of GCHQ, in September 1973. Soon after, Nick Patterson told Cocks about James H. Ellis' ''non-secret encryption,''The Open Secret
/ref> 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 number theory, integer factorization is the decomposition of a composite number into a product of smaller integers. If these factors are further restricted to prime numbers, the process is called prime factorization. When the numbers are s ...

, 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

. 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 1989 N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History ...
designing an open internet architecture for CERN, its adaptation and adoption for the Arpanet ... did public key cryptography realise its full potential. -
Ralph Benjamin Ralph Benjamin (17 November 1922 – 7 May 2019) was a British scientist and electrical engineer. Biography Benjamin was born in Darmstadt, Germany. He attended boarding school in Switzerland from 1937, and was sent to England in 1939 as a ...
GCHQ 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 ''Spycatcher: The Candid Autobiography of a Senior Intelligence Officer'' (1987) is a memoir written by Peter Wright, former MI5 officer and Assistant Director, and co-author Paul Greengrass. He drew on his own experiences and research in ...

'' 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 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. The first IMO was held in Romania in 1959. It has since been held annually, excep ...

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

University of Bristol , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

. 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 George I on 18 May 1725. The name derives from the elaborate medieval ceremony for appointing a knight, which involved bathing (as a symbol of purification) a ...

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 , mottoeng = Through efforts to heights , established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...

in 2015. With James Ellis and

Malcolm Williamson Malcolm Benjamin Graham Christopher Williamson, (21 November 19312 March 2003) was an Australian composer. He was the Master of the Queen's Music from 1975 until his death. Biography Williamson was born in Sydney in 1931; his father was an A ...

, 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 a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

(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 Modern cryptographers Fellows of the Royal Society Companions of the Order of the Bath International Mathematical Olympiad participants