Security Analysis And Improvement On Deterministic Random Bit Generators

Since random number are widely used in key pair generation, initialization vectors, nonce, random authentication challenges, key-agreement schemes, generating prime numbers and so on, it is vital in cryptography. Random Number or Bit Generator (RBG) is the algorithm, function or device which generates random number. Its security level impacts the whole crypto-system.The article mainly focuses on the Deterministic Random Bit Generator (DRBG, so called Pseudorandom Bit Generator). Firstly, precise definitions involving random number and analysis and summaries of the existing RBGs and their standards are given after which the discussion about cryptography algorithms used in RBGs are following. Secondly, the author conducts some analysis using statistics on DRBG Standard testing methods in order to prove their effectiveness and practical purpose. So, some mathematical researches on statistical random number generator test methods in Federal Information Processing Standard (FIPS) 140-1 are made. With help of paper material, the author discusses random number generator test methods in Special Publication (SP) 800-22 and figure out their statistical meanings.Moreover, the security analysis on recommended DRBGs in National Institute of Standards and Technology (NIST) SP 800-90 is showed. In the early Crypto 2007, a report says that there is a technique backdoor in that standard. The adversary (maybe the designer himself) can take advantage in it to attack the DRBG system. It is astonishing that a standard is with such a big problem. Based on that report, the article gives more details about the standard and show that serial conditions need be satisfied to make the attack to the Dual_EC_DRBG succeed through the mathematical deduction. Because of the complexity of Elliptic Curve Cryptography system, more background knowledge is given prior to the discussion.At last, the author analyzes a DRBG designed by him and used in a engineering project. Statistical properties and security discussions are given. All tests in FIPS 140-1 are conducted. And that DRBG passed all. It concludes that the pseudorandom bit sequence generated by that DRBG has great statistic distributions. The analysis shows that certain attack exists but hard to implement.