How does key size security compare between elliptic curves and RSA?

Cryptographic security level is measured in bits of security, indicating how many operations an attacker needs to perform to break a primitive. Different algorithms achieve equivalent security levels with drastically different key sizes. For instance, a 128-bit security level is considered roughly equivalent to using an RSA key of 3072 bits.

What we know

• Security level in cryptography is usually expressed as a number of bits of security, representing the power of two operations required for an attacker to break the primitive. [4]
• Using AES-128 with a 128-bit key is considered roughly equivalent in security level to using an RSA key with a 3072-bit key size. [4]
• Public-key algorithms widely rely on the difficulty of mathematical problems like integer factorization, the discrete logarithm problem, or the elliptic-curve discrete logarithm problem. [2]

Where to go next

• the bigger pictureWhat is post-quantum cryptography?
• how it workedHow does Shor's algorithm threaten current cryptography?
• whenWhat are NIST's Post-Quantum Cryptography Standards?
• compared withHow does Grover's algorithm affect symmetric ciphers?
• how we knowWhat is Mosca's theorem in cryptographic risk analysis?
• an unexpected connectionWhy might encrypted photographs be processed in cloud environments?Homomorphic encryption allows cloud services to compute on encrypted data without decrypting it, connecting key security principles directly to privacy-preserving outsourced storage.

Sources

• [1]post-quantum cryptography (Wikidata Q7233576) · CC0 1.0
• [2]Post-quantum cryptography · CC BY-SA 4.0
• [3]Comparison of TLS implementations · CC BY-SA 4.0
• [4]Security level · CC BY-SA 4.0
• [5]Homomorphic encryption · CC BY-SA 4.0

Your path

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