![]() ![]() Addition and multiplication must be commutative: so a + b = b + a and similarly for multiplication.Addition and multiplication must be associative: so a + (b + c) = (a + b) + c and similarly for multiplication. ![]() Both addition and multiplicaiton are closed over the set, so for example if a and b are in the set then so are a + b and a * b.In order to be a field the following conditions also have to be met: The elements could be numbers, or they could be something else entirely. In essence a field is a set of elements with operations defined for the elements of that set that equate to something like addition, substraction, multiplication and division. We need to define what is meant by a field. However, with elliptic curve algorithms, the equivalent key length is 512 bits, which is entirely practical.įirst of all some terminology. Keys of this size are typically not practical due to the amount of processing power that would be required, and therefore the speed of the operations. As can be seen, to get equivalent strength to a 256 bit symmetric key, a standard asymmetric algorithm would have to use an enormous key of 15360 bits. ![]()
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