Elliptic Curve Cryptography (ECC) Questions

For cybersecurity professionals, here’s a quick quiz on ECC (Elliptic Curve Cryptography):

1. Who was a co-inventor of ECC:
A. Neal Koblitz
B. Ron Rivest
C. Adi Shamir
D. Shafi Goldwasser
E. Tahir ElGamal

2. Which curve did Satoshi Nakamoto select for Bitcoin:
A. secp128r1
B. secp160r1
C. secp256k1
D. secp256r1
E. secp521r1

3. Which curve is used for P256 — as used in TLS:
A. secp128r1
B. secp160r1
C. secp256k1
D. secp256r1
E. secp521r1

4. Which curve gives has 256-bit equivalent security:
A. secp128r1
B. secp160r1
C. secp256k1
D. secp256r1
E. secp521r1

5. Which is true about a private key in ECC:
A. It is a random scalar value
B. It is a non-changing scalar value
C. It is a point on the curve

6. Which is true about a public key in ECC:
A. It is a random scalar value
B. It is a non-changing scalar value
C. It is a point on the curve

7. Which signing method is used in Bitcoin and Ethereum:
A. EDCSA
B. EdDSA
C. RSA
D. ElGamal

If you answered A, C, D, E, A, C and A, well done. If not, perhaps review some details of ECC: https://asecuritysite.com/cryptojs/crytojs_ecc

Speed differences

What’s the difference in performance for key pair generation between RSA and ECC?

For RSA key pair generation with 128-bit security, we often use RSA-2048. On my browser, the key is generated in around 509 ms: https://asecuritysite.com/cryptojs/crytojs_rsa

RSA 2048
Key generated in 509 ms
 - - -BEGIN RSA PRIVATE KEY - - -
MIIEowIBAAKCAQEAjaCSVASnAt35AOOwh+FfcmB6ZIm8TL1yv5CemDko1KYqI3sa
kp2w1cpkO4bkPz3C8Kj5A69N+MF0KV/PoevqdjbkmabR+4I+v12k6bPQXzdVKji+
cpiyYJj5+j32ah9rQfhMYXnfCAmQcmfIVGhgjdEyNg+kYrFqLn1yvZEAUD3Kht4m
XGxoqI/9x/OzCYrelL+/BQKfzU3urT1pVR1j3kcQbuQWsEtpU/ptWWuB3YJMeaMR
NCnvkh1JYaeUHki9VUgglsmG7oACTwuf2pUnaEeEONxy3eUKWx77L8R6SXkNBvB+

For ECC key generation with 128-bit security, we often use secp256k1. On my browser, the key is generated in 27 ms: https://asecuritysite.com/cryptojs/crytojs_ecc

Type: secp256k1
Public Key generated in 27 ms
Private key: 22164275389021716382923025745693202919058804796279573027267140115072225880733
Public key(x): 13906234413559224920779302781113749485619109983789020983495760922310038582610
Public key(y): 112984163251306409982500288777459751254626639566987999473015510607892097654131
==Parameters====
a: 0
b: 7
Gx: 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy: 32670510020758816978083085130507043184471273380659243275938904335757337482424

ECC is thus at least 10 times faster for key pair generation than the equivalent RSA method.