What are the vulnerabilities of elliptic curve cryptography?

Elliptic curve cryptography relies on algebraic structures over finite fields to provide security with smaller keys. Vulnerabilities in specific implementations can emerge, such as flawed pseudo-random generators. Notably, the Dual EC DRBG standard was criticized and withdrawn due to concerns that it contained a National Security Agency backdoor.

What we know

• Elliptic-curve cryptography is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. [2]
• The Dual EC DRBG algorithm was presented as a cryptographically secure pseudorandom number generator using elliptic curve cryptography methods. [5]
• Dual EC DRBG faced wide public criticism, including the identification of a possible backdoor placed by the National Security Agency. [5]
• Despite criticism, Dual EC DRBG was one of four standardized pseudorandom number generators in NIST SP 800-90A for seven years until it was withdrawn. [5]

Where to go next

• how it workedHow does key agreement work using elliptic curves?
• what caused itWhat led to the withdrawal of the Dual EC DRBG standard?
• compared withHow does elliptic curve cryptography compare to RSA?
• a case in pointWhat is the Elliptic Curve Digital Signature Algorithm?
• the bigger pictureWhat is public-key cryptography?
• an unexpected connectionHow did a random number generator become a vulnerability vehicle?A cryptographically secure pseudorandom number generator standardized by NIST for years was widely criticized and eventually withdrawn due to suspected agency backdoors.

Sources

• [1]elliptic curve cryptography (Wikidata Q1048911) · CC0 1.0
• [2]Elliptic-curve cryptography · CC BY-SA 4.0
• [3]Elliptic Curve Digital Signature Algorithm · CC BY-SA 4.0
• [4]Elliptic-curve Diffie–Hellman · CC BY-SA 4.0
• [5]Dual EC DRBG · CC BY-SA 4.0

Your path

1. What is the Hebrew Bible and how was it made?
2. /Who was Joachim Murat?
3. /What is the Rano Raraku quarry on Easter Island?
4. /What are the vulnerabilities of elliptic curve cryptography?