Abstract
The design of cryptographically secure pseudorandom number generator (CSPRNG) producing unpredictable pseudorandom sequences robustly and credibly has been a nontrivial task. Almost all the chaos-based CSPRNG design approaches invariably depend only on statistical analysis. Such schemes designed to be secure are being proven to be predictable and insecure day by day. This paper proposes a design and instantiation approach to chaos-based CSPRNG using proven generic constructions of modern cryptography. The proposed design approach with proper instantiation of such generic constructions eventually results in providing best of both worlds that is the provable security guarantees of modern cryptography and passing of necessary statistical tests as that of chaos-based schemes. Also, we introduce a new coupled map lattice based on logistic-sine map for the construction of CSPRNG. The proposed pseudorandom number generator is proven using rigorous security analysis as that of modern cryptography and tested using the standard statistical testing suites. It is observed that the generated sequences pass all stringent statistical tests such as NIST, Dieharder, ENT, and TestU01 randomness test suites.
Highlights
Secure pseudorandom number generator (CSPRNG) efficiently generates sequences that cannot be distinguished from random sequences by efficient adversaries. e number of hardware and software implementations of Cryptographically secure pseudorandom number generator (CSPRNG) based on chaotic maps has increased recently along with chaos-based cryptosystems
We show in this paper that the sequences generated are computationally indistinguishable and hard to predict in the presence of efficient adversaries using modern cryptography design tools
(2) We prove through theoretical security analysis methodology using modern cryptography tools that δ is an unpredictable function and subsequently, we prove the pseudorandomness of construction G as required by modern cryptography
Summary
Secure pseudorandom number generator (CSPRNG) efficiently generates sequences that cannot be distinguished from random sequences by (computationally) efficient adversaries. e number of hardware and software implementations of CSPRNG based on chaotic maps has increased recently along with chaos-based cryptosystems. E proven modern cryptographic constructions such as Merkle–Damgard, sponge construction, and block cipher modes can be used by instantiating such proven constructions with suitable chaos-based functions Such design approach will reduce the reliance of security assessment methods on statistical analysis. Erefore, beyond statistical analysis, the design approach for chaos-based cryptographic design should be based more on instantiating proven constructions with chaotic maps as unpredictable functions rather designing new constructions on each proposed chaotic cryptographic algorithm. Considering all the above factors, we demonstrate a design approach by instantiating a proven modern cryptographic PRNG construction with a new chaotic map based on coupled map lattices, prove its security using modern cryptographic attack models, and perform statistical analysis on the output.
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