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ECC Security Level Calculator

Convert an elliptic-curve field size into security bits, the RSA modulus that matches it, and key and signature sizes.

About ECC Security Level Calculator

The best known attack on a well-chosen curve is a generic square-root discrete-log search, so a 256-bit curve costs about 2^128 group operations to break. Point encodings follow SEC 1: a leading tag byte plus one or both affine coordinates padded to the field length. P-256 delivers RSA-3072 strength in a 65-byte public key and a 64-byte signature, which is why TLS 1.3, SSH and code signing all default to elliptic curves on constrained links.

Formula

ECC Security Level

security strength ≈ field size ÷ 2 (Pollard rho), so P-256 ≈ 128-bit and P-384 ≈ 192-bit; an uncompressed point is 2 × ⌈field ÷ 8⌉ + 1 bytes.

field size
Bit length of the curve's prime field
security bits
Equivalent symmetric strength
0x04 byte
The leading tag on an uncompressed point

Worked example

With the default values below, ECC Security Level Calculator returns Security Strength of 128. Change any input above and every figure here is recalculated in your browser.

Inputs used

Curve field sizeone of P-224 / secp224r1, P-256 / secp256r1, P-384 / secp384r1, P-521 / secp521r1
P-256 / secp256r1

Results

Security Strength
128 bits
Equivalent RSA Modulus
3,072 bits
Uncompressed Public Key
65 bytes
Compressed Public Key
33 bytes
Raw ECDSA Signature
64 bytes
Assessment
Modern baseline — 128-bit strength

Step by step

  1. 1Values used
  2. 2ECC Security Level
  3. 3Security Strength= 128 bits
  4. 4Equivalent RSA Modulus= 3,072 bits
  5. 5Uncompressed Public Key= 65 bytes
  6. 6Compressed Public Key= 33 bytes
  7. 7Raw ECDSA Signature= 64 bytes
  8. 8Assessment= Modern baseline — 128-bit strength

Assumptions and limits

  • The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is ECC Security Level calculated?

security strength ≈ field size ÷ 2 (Pollard rho), so P-256 ≈ 128-bit and P-384 ≈ 192-bit; an uncompressed point is 2 × ⌈field ÷ 8⌉ + 1 bytes. The best known attack on a well-chosen curve is a generic square-root discrete-log search, so a 256-bit curve costs about 2^128 group operations to break. Point encodings follow SEC 1: a leading tag byte plus one or both affine coordinates padded to the field length.

Why does ECC Security Level matter?

P-256 delivers RSA-3072 strength in a 65-byte public key and a 64-byte signature, which is why TLS 1.3, SSH and code signing all default to elliptic curves on constrained links.

What values do I need to enter?

This calculator takes 1 input: Curve field size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

Why does P-521 give 256-bit security rather than 260?

Security levels are quoted at the standard rungs of 112, 128, 192 and 256 bits. P-521's raw ~260-bit work factor is rounded down to the 256-bit rung so it can be paired sensibly with AES-256 and SHA-512.

Related Calculators

ECC Security Level Calculator – Calculate Security Strength