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RSA Key Strength Calculator

Work out rsa key strength instantly with clear inputs, formula shown and shareable results.

About RSA Key Strength Calculator

RSA security grows very slowly with modulus size because the general number field sieve is sub-exponential: doubling from 2048 to 4096 bits adds only about 28 bits of security while private-key operations get roughly eight times more expensive, since modular exponentiation scales with the cube of the modulus length. That poor trade-off is the main reason new deployments favour elliptic curves.

Formula

RSA cost and strength

private-key cost scales as (bits / 2048)^3; security level from NIST SP 800-57: 2048 -> 112 bits, 3072 -> 128 bits, 15360 -> 256 bits

Worked example

With the default values below, RSA Key Strength Calculator returns Effective security level of 112. Change any input above and every figure here is recalculated in your browser.

Inputs used

RSA modulus sizeaccepts 512–16,384 bits
2,048 bits
Signature operations needed per secondminimum 0.1
500

Results

Effective security level
112 bits
Private-key operation cost relative to RSA 2048
1.00 x
CPU cores to sustain the signing rate
0.33
Standards status
Acceptable until about 2030 per NIST SP 800-57

Step by step

  1. 1Values used
  2. 2RSA cost and strength
  3. 3Effective security level= 112 bits
  4. 4Private-key operation cost relative to RSA 2048= 1.00 x
  5. 5CPU cores to sustain the signing rate= 0.33
  6. 6Standards status= Acceptable until about 2030 per NIST SP 800-57

Assumptions and limits

  • The result is derived only from the 2 inputs 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 2 decimal places, 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

Should I move from RSA 2048 to 4096?

Only where policy demands it. The extra strength is modest and the cost is large; moving to ECDSA P-256 or Ed25519 gives 128-bit security at a fraction of the compute.

Why is the public operation cheap?

The public exponent is normally 65537, which requires only 17 squarings and one multiplication. Verification is therefore hundreds of times faster than signing.

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