# Linear time multiplication on RAM machine?

Integer Multiplication has an O-optimal linear-time algorithm on a RAM or SMM

Is this page fooling me or how can we multiply 2 numbers in linear time (bitwise complexity) using RAM?

• Why do you think the page is talking about bit complexity? – Yuval Filmus Sep 9 '17 at 10:21
• Because when speaking of words it takes $O(1)$ time. – rus9384 Sep 9 '17 at 11:05

Theorem 6.1 There exists an SMM which performs integer-multiplication in linear time, i.e. there is a constant $c$ such that any $2N$-bit input is read as the concatenation of two $N$-bit integers $x$, $y$, and after at most $cN$ many steps their product $z=xy$ is output in binary representation.