Why Can We Use "Shorter" Keys?: Key Length vs Security Bits, the Real Story

"ECDSA P-256 has shorter keys than RSA-2048. So it must be weaker." ...I used to think that too. 2048 bits vs 256 bits. Just looking at the numbers, RSA seems 8x "stronger." But NIST (the National Institute of Standards and Technology) treats these two as equal in security strength. On top of that,