ECC Size Budget Calculation Audit

ECC Size Budget Calculation Audit

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

ECC Size Budget Calculation Audit

The chapter compares key sizes: a 256-bit elliptic-curve key is just 32 bytes, while an RSA modulus at the same security needs 3072 bits, or 384 bytes — a 12-times difference of 352 bytes. Those repeated bytes matter on radio airtime and small-device memory. This audit works the ECC size budget, keeping the 128-bit security target separate from the key-size field.

Companion to the chapter Elliptic-Curve Cryptography for IoT — every number here comes from that chapter.

The chapter's security claim is qualitative, but the footprint claim is arithmetic. Keep the 256-bit curve size, the 3072-bit RSA comparison, and the approximate 128-bit security target as separate facts.

See the relationship before changing it

The figure reads from left to right. The blue card is curve key size. The middle card applies the page rule. The green card is encoded key size. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

Walk the arrows. This conversion measures field size only. It does not prove equal security between algorithms.

Derive the baseline in four named moves

1. 1

   Name the input. The chapter baseline is 256 bits.

2. 2

   Name the relationship. bytes = bits / 8

3. 3

   Substitute with units. 256 bits / 8 = 32.00 bytes

4. 4

   Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change curve key size

Try Predict the direction of bytes = bits / 8. Test another curve key size, then compare encoded key size.

Curve key size

256 bits

Chapter baseline

Encoded key size

Observe This conversion measures field size only. It does not prove equal security between algorithms. Reset curve key size to 256 and compare encoded key size.

Explain This conversion measures field size only. It does not prove equal security between algorithms.

Check yourself

What should you do before trusting a moved-control result?

Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.

What does this small model leave out?

Answer: Only curve key size moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only curve key size. It is not a field prediction.

TryPress Check derivation to convert a 256-bit elliptic-curve key and 3072-bit RSA modulus into bytes.

ObserveThe conversions yield 32 B and 384 B: the modulus field is 12× larger, a difference of 352 B.

ExplainThe stated 128-bit value is an approximate classical security strength for the comparison, not the encoded length of either public-key field.

Audit step	Arithmetic from the chapter	Design implication
Curve key raw scalar size	256 bits / 8 = 32 bytes	The ECC key-size figure fits the small-key intuition for constrained storage and messages.
RSA modulus raw size	3072 bits / 8 = 384 bytes	The RSA comparison is much larger before certificates, signatures, encodings, and protocol framing are counted.
Size ratio	3072 / 256 = 12	The raw RSA modulus is 12 times the curve-key bit count used in the chapter's comparison.
Raw byte difference	384 - 32 = 352 bytes	Those 352 bytes are the kind of repeated overhead that matters on radio airtime and small device memory budgets.

The 128-bit figure names the approximate classical security target for this comparison; it is not the same as the number of bits carried in a key-size field.

Technical boundaries
The size budget deliberately does not simulate certificate, signature, public-key encoding, protocol framing, compute time, side channels, or implementation security; it compares raw key and modulus bit lengths at the stated security target.

Work the audit first, then check the displayed derivation.

Every number above is taken from the chapter’s own material and re-derived step by step.