Applied Cryptography
In the table of NIST SP 800-57, which of the following is the combination of RSA key length (the number of bits of n) and elliptic-curve key length given as the guideline for security comparable to a 128-bit symmetric-key cipher (AES-128)?
- AAbout 128 bits for RSA and about 128 bits for elliptic-curve cryptography
- BAbout 2048 bits for RSA and about 128 bits for elliptic-curve cryptography
- CAbout 3072 bits for RSA and about 256 bits for elliptic-curve cryptography
Show answer and explanation
Answer: C. About 3072 bits for RSA and about 256 bits for elliptic-curve cryptography
Public-key cryptography needs longer keys than symmetric-key cryptography to achieve the same security. In the table of NIST SP 800-57 Part 1, the guideline for 128-bit security is 3072 bits for RSA and 256 to 383 bits for elliptic-curve cryptography. For elliptic-curve cryptography the best known attacks take effort of about half the key length in bits, so a key of about twice the number of security bits suffices, giving the same security with a much shorter key than RSA. 2048-bit RSA is the guideline for 112-bit security.
- A. In public-key cryptography the number of key bits does not directly equal the number of security bits.
- B. 2048-bit RSA corresponds to 112 bits. A 128-bit elliptic-curve key gives only about 64-bit security.
- C. Correct. These are the guideline values given in the table.