Elliptic curve parameters What's the meaning of "160-bit curve" in an elliptic curve? Or 192, 224, 256, etc. And what is the standard for selecting this number of bits?

Why they don't say "100-bit curve"?
What's the meaning of 160 bit Curve in Elliptic curve?


It's the size of the field, as the other answers explain. It affects the size of keys and signatures (which can be equal to the number or e.g. double it), as well as security and performance.


  Why they don't say 100 bit curve?


100-bit curves are too small.

It's also a convention. Other cryptographic primitives, like hash functions or symmetric ciphers, can have any bit length we want and powers of two are chosen for performance. So we want elliptic curves that match (or are close) to pair with them in a protocol, so we don't waste performance on security beyond the weakest link.

There's also the performance of the elliptic curve algorithm itself. It is useful to have the bit length be a multiple of a large enough power of two, like 64 bits, because computers deal with numbers of 32-bits or 64-bits. This isn't always the case though (e.g. P-521) if there happens to be a very juicy prime ($2^{521}-1$) that is easy to work with.

(As an aside, we do sometimes approximate something as e.g. 100-bit security if we don't care about the exact number but only a minimum. For example, a 256-bit elliptic curve that has a prime smaller than $2^{256}$ – e.g. P-256 – has only approximately 128-bit security so might as well call it 100-bit. Especially after you add a signature algorithm that also relies on a hash function, perhaps losing another bit of security to collisions.)