The National Institute of Standards and Technology (NIST) recommended elliptic curve domain parameters to have names such as “secp…” and “sect…”.
For example: “secp224k1” and “sect571k1”.
What is the difference between “secp…” and “sect…”?
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The sect curves are curves over a binary field. From SEC 2: Recommended Elliptic Curve Domain Parameters (chapter 3):
The example elliptic curve domain parameters over $\mathbb{F}_{2^m}$ have been given nicknames to enable them to be easily identified. The nicknames were chosen as follows. Each name begins with sec to denote ‘Standards for Efficient Cryptography’, followed by a $t$ to denote parameters over $\mathbb{F}_{2^m}$ , followed by a number denoting the field size $m$, followed by a $k$ to denote parameters associated with a Koblitz curve or an $r$ to denote verifiably random parameters, followed by a sequence number.
While the secp curves are over fields over a prime field - or $\mathbb{F}_p$ in mathematical representation. Please read elliptic curve tutorials to understand the difference between the calculations for prime and binary fields.
answered Oct 3, 2014 at 20:25
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$\begingroup$ Note that the field size for curves is usually taken to be equal to the effective key size (and it is actually the size of the secret value, but the public key is larger). Keys can be encoded in different ways, and their binary notation will often not directly reflect the key size. $\endgroup$– Maarten Bodewes ♦Oct 3, 2014 at 20:36