Sinkov statistics, also known as log-weight statistics, is a specialized field of statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 that was developed by Abraham Sinkov

Abraham Sinkov

Dr. Abraham Sinkov was a US cryptanalyst.-Biography:Sinkov, the son of immigrants from Russia, was born in Philadelphia, but grew up in Brooklyn. After graduating from Boys High School—what today would be called a "magnet school" -- he took his B.S. in mathematics from City College of New York...

, while working for the small Signal Intelligence Service organization, the primary mission of which was to compile code

Code

A code is a rule for converting a piece of information into another form or representation , not necessarily of the same type....

s and cipher

Cipher

In cryptography, a cipher is an algorithm for performing encryption or decryption — a series of well-defined steps that can be followed as a procedure. An alternative, less common term is encipherment. In non-technical usage, a “cipher” is the same thing as a “code”; however, the concepts...

s for use by the U.S. Army

United States Army

The United States Army is the main branch of the United States Armed Forces responsible for land-based military operations. It is the largest and oldest established branch of the U.S. military, and is one of seven U.S. uniformed services...

. The mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

 involved include modular arithmetic

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus....

, a bit of 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...

, some linear algebra

Linear algebra

Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...

 of two dimensions with matrices

Matrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

, some combinatorics

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

, and a little statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

.

Sinkov did not explain the theoretical underpinnings of his statistics, or characterized its distribution

Distribution (mathematics)

In mathematical analysis, distributions are objects that generalize functions. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative...

, nor did he give a decision procedure for accepting or rejecting candidate plaintext

Plaintext

In cryptography, plaintext is information a sender wishes to transmit to a receiver. Cleartext is often used as a synonym. Before the computer era, plaintext most commonly meant message text in the language of the communicating parties....

s on the basis of their S₁ scores. The situation becomes more difficult when comparing strings

String (computer science)

In formal languages, which are used in mathematical logic and theoretical computer science, a string is a finite sequence of symbols that are chosen from a set or alphabet....

of different lengths because Sinkov does not explain how the distribution of his statistics changes with length, especially when applied to higher-order grams. As for how to accept or reject a candidate plaintext, Sinkov simply said to try all possibilities and to pick the one with the highest S₁ value. Although the procedure works for some applications, it is inadequate for applications that require on-line decisions. Furthermore, it is desirable to have a meaningful interpretation of the S₁ values.