Security
The stated purpose of including the Dual_EC_DRBG in NIST SP 800-90 is that its security is based on a hard problem from number theory, such as the elliptic curve Decision Diffie-Hellman problem. Given the importance of having secure random number generators in cryptography, in certain cases it may be desirable to sacrifice speed for security.
Subsequent to publication of the Dual_EC_DRBG algorithm, various researchers have reported certain security issues with the properties of the Dual_EC_DRBG:
- The intermediate values it generates, a sequence of elliptic curve points, should, under certain reasonable assumptions, such as the Decision Diffie-Hellman problem, be indistinguishable from uniformly random elliptic curve points.
- The sequence of bits generated from the Dual_EC_DRBG, under certain parameter choices, can be distinguished from uniformly random bits, making its output unsuitable for use as a stream cipher, and, arguably, for more general use.
- Its security requires that a certain problem be hard, such as the computational Diffie-Hellman problem, but one of the recommended configurations of the Dual_EC_DRBG permits the possibility that a key, which facilitates solution of the problem, has been retained. See the Controversy section for more discussion.
Read more about this topic: Dual EC DRBG
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