# Chris Christensen Northern Kentucky University. B.A. in mathematics from Columbia in 1911. Masters degree 1913. Ph.D. from Yale in 1926. 1916 joined US.

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Chris Christensen Northern Kentucky University

B.A. in mathematics from Columbia in 1911. Masters degree 1913. Ph.D. from Yale in 1926. 1916 joined US Navy Reserves and served in World War I as a LT (j.g.)

Hill joined the faculty at Hunter College in 1927. Taught at the Army University in Biarritz, France in 1945. Hill remained at Hunter until his retirement due to illness in 1960. Hill died in 1961.

David Kahn met with Hills widow after Hills death and collected papers of Hills that were laying around the house. Those papers are now at the National Cryptologic Museum library.

1929 Cryptography in an algebraic alphabet 1931 Concerning certain linear transformation apparatus of cryptography

Monoalphabetic substitutionPolygraphic substitution

Reference The keyspace of the Hill cipher by Overby, Traves, and Wojdylo in Cryptologia, 2005. 4x4 key

Its LINEAR.

Solution is NP-hard.

Amount \$128 Check number 586 Date December 26, 1928

Data from a check Amount \$128 1 28 Check number 586 5 86 Date December 26, 1928 26 28 56 99 01 12 72 64 Data from a chart

Input is 6 numbers between 00 and 100 56 99 01 12 72 64 101^6 = 1,061,520,150,601 Output is 3 numbers between 00 and 100 100 40 68 101^3 = 1,030,301

In 1926 and 1927, while he was a Ph.D. student at Yale, Hill published three papers in Telegraph and Telephone Age which describe a checking scheme. He hoped to make some money from his checking scheme, which he was seeking to have patented. This did not go anywhere, but it sparked his interest in secret communications. David Kahn

Briefly stated, what I now have in mind – and have not noticed hitherto – is that, if my checking procedure were applied generally, it would be very easy to make the telephone (long distance) take over effectively, in a novel way, a goodly portion of the present domestic telegraph business.

We are not interested in the origin or significance of the component parts of the number, nor in the method of transmittal. Thus, 7405 might be a sum of money, and 000090 a combination of testing figures compounded from the initials to whom the money is being sent and from other elements; 98460 might refer to an entry in some code book or other volume, etc. The entire number may be sent as it stands, or by means of code and cipher. Our object here is merely to supply a check upon the accurate transmittal.

The nine-digit message is checked by the sequence 97 90 39. The sender send the message 984600007405000090 appended by the check 979039. The receiver calculates the check string from the received message string and compares it to the received check string. If the two check strings are the same, it is assumed that the message was transmitted without error.

All error detecting codes require some repetition of message information. The goal is to minimize the amount of repetition.

Error detecting codes The history of error detecting codes is not clear. Claude Shannon (1948) Richard Hamming (1948) Marcel Golay (1949) Error correcting codes

It is not clear from Hills Telegraph and Telephone Age papers whether he understood that the method he was describing was matrix multiplication. The checking of the accuracy of transmittal of telegraphic communications by means of operations in finite fields Undated; in the David Kahn collection.

My correspondent will be absolutely sure that he has precisely the message which I sent him, or absolutely sure that a mistake is present. … And nobody in the world except my correspondent can possibly decipher the meaning of my message. Moreover, my correspondent will be deadly sure, if the message checks, that message was sent by me and nobody else in the world. If this message checks, … correspondent can accept it as having all of my authority behind it.

Secret communications. Integrity. Authentication and non-repudiation.

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