Ada Audits the ECC Size Budget

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

ADA · CALCULATION AUDIT

Ada Audits the ECC Size Budget

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.

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.

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