Clifford Cocks
Encyclopedia
Clifford Christopher Cocks, CB
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 mediæval ceremony for creating a knight, which involved bathing as one of its elements. The knights so created were known as Knights of the Bath...

, (born 28 December 1950
) is a British mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 and cryptographer at GCHQ.
He invented the widely-used encryption algorithm now commonly known as RSA, about three years before it was independently developed by Rivest, Shamir
Adi Shamir
Adi Shamir is an Israeli cryptographer. He is a co-inventor of the RSA algorithm , a co-inventor of the Feige–Fiat–Shamir identification scheme , one of the inventors of differential cryptanalysis and has made numerous contributions to the fields of cryptography and computer...

, and Adleman
Leonard Adleman
Leonard Max Adleman is an American theoretical computer scientist and professor of computer science and molecular biology at the University of Southern California. He is known for being a co-inventor of the RSA cryptosystem in 1977, and of DNA computing...

 at MIT
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

. He has not been generally recognised for this achievement because his work was by definition classified information
Classified information
Classified information is sensitive information to which access is restricted by law or regulation to particular groups of persons. A formal security clearance is required to handle classified documents or access classified data. The clearance process requires a satisfactory background investigation...

, and therefore not released to the public at the time.

Life

In 1968, Cocks won Silver at the International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate 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, except in 1980...

 while at Manchester Grammar School
Manchester Grammar School
The Manchester Grammar School is the largest independent day school for boys in the UK . It is based in Manchester, England...

. Cocks went on to study mathematics as an undergraduate at King's College, Cambridge
King's College, Cambridge
King's College is a constituent college of the University of Cambridge, England. The college's full name is "The King's College of our Lady and Saint Nicholas in Cambridge", but it is usually referred to simply as "King's" within the University....

 and then did graduate work at the University of Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...

, where he specialised in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...

, but left to join CESG, an arm of GCHQ, in September 1973.

At GCHQ, Cocks was told about James H. Ellis
James H. Ellis
James Henry Ellis was a British engineer and mathematician. In 1970, while working at the Government Communications Headquarters in Cheltenham he conceived of the possibility of "non-secret encryption", more commonly termed public-key cryptography.-Early life, education and career:Ellis was born...

' "non-secret encryption" and further that since it had been suggested in the late 1960s, no one had been able to find a way to actually implement the concept. Cocks was intrigued, and invented, in 1973, what has become known as the RSA encryption algorithm, realising Ellis' idea. GCHQ appears not to have been able to find a way to use the idea, and in any case, treated it as classified information
Classified information
Classified information is sensitive information to which access is restricted by law or regulation to particular groups of persons. A formal security clearance is required to handle classified documents or access classified data. The clearance process requires a satisfactory background investigation...

, so that when it was reinvented and published by Rivest, Shamir, and Adleman in 1977, Cocks' prior achievement remained unknown until 1997.

In 2001, Cocks developed one of the first secure identity based encryption
ID-based cryptography
ID-based encryption is an important primitive of ID-based cryptography. As such it is a type of public-key encryption in which the public key of a user is some unique information about the identity of the user...

 (IBE) schemes, based on assumptions about quadratic residues in composite groups. The Cocks IBE scheme
Cocks IBE scheme
Cocks IBE scheme is an Identity based encryption system proposed by Clifford Cocks in 2001 . The security of the scheme is based on the hardness of the quadratic residuosity problem.-Setup:The PKG chooses:...

 is not widely used in practice due to its high degree of ciphertext expansion
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 include a message-unique Initialization Vector...

. However, it is currently one of the few IBE schemes which do not use bilinear pairings
Pairing
The concept of pairing treated here occurs in mathematics.-Definition:Let R be a commutative ring with unity, and let M, N and L be three R-modules.A pairing is any R-bilinear map e:M \times N \to L...

, and rely for security on more well-studied mathematical problems.

As of 2003, Clifford Cocks held the post of Chief Mathematician at GCHQ. He was made a Companion of the Order of the Bath
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 mediæval ceremony for creating a knight, which involved bathing as one of its elements. The knights so created were known as Knights of the Bath...

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

See also

  • List of multiple discoveries (see "RSA")

External links

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