In mathematics, the function field sieve was introduced in 1994 by Adleman as an efficient technique for extracting discrete logarithm

Discrete logarithm

In mathematics, specifically in abstract algebra and its applications, discrete logarithms are group-theoretic analogues of ordinary logarithms. In particular, an ordinary logarithm loga is a solution of the equation ax = b over the real or complex numbers...

s over finite field

Finite field

In abstract algebra, a finite field or Galois field is a field that contains a finite number of elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory...

s of small characteristic

Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char, is defined to be the smallest number of times one must use the ring's multiplicative identity element in a sum to get the additive identity element ; the ring is said to have characteristic zero if this repeated sum never reaches...

, and elaborated by Adleman and Huang in 1999.

Sieving for points at which a polynomial

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

-valued function is divisible by a given polynomial is not much more difficult than sieving over the integers – the underlying structure is fairly similar, and Gray code

Gray code

The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one bit. It is a non-weighted code....

provides a convenient way to step through multiples of a given polynomial very efficiently.

The Adleman–Huang paper is available at Science Direct, but views the problem using very algebraic-geometric language.