Robust Pseudo-Random Number Generators with Input Secure Against Side-Channel Attacks

International audienceA pseudo-random number generator (PRNG) is a deterministic algorithm that produces numbers whose distribution is indistinguishable from uniform. In this paper, we extend the formal model of PRNG with input defined by Dodis et al. at CCS 2013 to deal with partial leakage of sensitive information. The resulting security notion, termed leakage-resilient robust PRNG with input, encompasses all the previous notions, but also allows the adversary to continuously get some leakage on the manipulated data. Dodis et al. also proposed an efficient construction, based on simple operations in a finite field and a classical deterministic pseudo-random generator G. Here, we analyze this construction with respect to our new stronger security model, and prove that with a stronger G, it also resists leakage. We show that this stronger G can be obtained by tweaking some existing constructions based on AES. We also propose a new instantiation which may be better in specific cases. Eventually, we show that the resulting scheme remains quite efficient in spite of its new security properties. It can thus be recommended in contexts where side-channel resistance is required

SoK: Security Models for Pseudo-Random Number Generators

Randomness plays an important role in multiple applications in cryptography. It is required in fundamental tasks such as key generation, masking and hiding values, nonces and initialization vectors generation. Pseudo-random number generators have been studied by numerous authors, either to propose clear security notions and associated constructions or to point out potential vulnerabilities. In this systematization of knowledge paper, we present the three notions of generators that have been successively formalized: standard generators, stateful generators and generators with input. For each notion, we present expected security properties, where adversaries have increasing capabilities (including access to partial information on the internal variables) and we propose secure and efficient constructions, all based on the block cipher AES. In our description of generators with input, we revisit the notions of accumulator and extractor and we point out that security crucially relies on the independence between the randomness source and the seeds of the accumulator and the extractor. To illustrate this requirement, we identify a potential vulnerability of the NIST standard CTR_DRBG