# How does Poly1305 use $2^{130}-5$?

How is the number $2^{130}-5$ used in Poly1305? It operates on blocks that are 128 bits long, but the number has 130 bits. I don't understand how it is used. This comment makes me think it uses integer arithmetic.

• The complete details of the format are given in the paper on p. 4, and the one-line Poly1305 formula is then given on p. 5. I recommend reading that—you don't have to follow the whole paper to understand those two pages. The even briefer summary is that the bit string message is padded and broken into 129-bit chunks that are interpreted as unsigned little-endian integers. – Squeamish Ossifrage Feb 9 '18 at 5:16
• There's also this explanation if you're less familiar with the background. – SAI Peregrinus Feb 9 '18 at 14:42