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Boolean functions play essential roles in certain symmetric cryptographic schemes and error-correcting codes. Apart from the cryptographic criteria satisfied by Boolean functions, constructions of functions with few Walsh spectral value are also of particular interests in cryptographic applications. Due to the problem that the five-value spectrum functions with duals being not basic plateaued functions remains to be answered, in this paper we intend to investigate the construction on non-basic plateaued duals of five-value spectrum functions. The issue of constructing non-basic totally disjoint spectra plateaued functions is dealt with from two aspects. We firstly address the characterization of non-basic plateaued functions corresponding to Walsh supports with unequal cardinality. Then the necessary and sufficient conditions of the spectral design of a partially non-basic five-value spectrum function are proposed. Meanwhile, we also provide the sufficient condition for constructing a valid five-value spectrum function whose duals are both defined on non-affine subspaces. Finally, the design of totally disjoint spectra functions on non-affine subspaces with equal cardinality is also studied. [ABSTRACT FROM AUTHOR]

Hedged public-key encryption (HPKE), introduced by Bellare et al. (ASIACRYPT 2009), provides useful security when the per-message randomness fails to be uniform due to faulty implementations or adversarial actions. The HPKE scheme achieves IND-CPA (chosen plaintext attack) security when the randomness they used is of high quality, but, when the randomness is poor quality, rather than breaking completely, it achieves a weaker but a useful notion of security called IND-CDA (chosen distribution attack) as long as the message and randomness together have sufficient min-entropy. However, little research on HPKE in the presence of key leakage was done. In this paper, we study HPKE featuring key leakage-resilience and formulate appropriate security notion for key leakage-resilient HPKE. We work in the continual key leakage model where the secret key is refreshed periodically and an adversary can learn arbitrary but bounded leakage on the secret key between the updates. We present two generic constructions of continual leakage-resilient HPKE in the standard model by using a continual leakage-resilient all-but-one lossy trapdoor function. Finally, we give an instantiation of leakage-resilient HPKE under the linear assumption in bilinear groups. [ABSTRACT FROM AUTHOR]