SUMMARYIn this paper, we investigate a relationship between the length-decreasing self-reducibility and the many-one-like reducibilities for partial multivalued functions. We show that if any parsimonious (manyone or metric many-one) complete function for NPMV (or NPMV g ) is length-decreasing self-reducible, then any function in NPMV (or NPMV g ) has a polynomial-time computable refinement. This result implies that there exists an NPMV (or NPMV g )-complete function which is not lengthdecreasing self-reducible unless P = NP.
The password-protected secret sharing (PPSS, for short) and its security notion, called in this paper the PPSSsecurity, were proposed by Bagherzandi, Jarecki, Saxena and Lu. However, another security notion for PPSS schemes, the pparam-security was proposed by Hasegawa, Isobe, Iwazaki, Koizumi and Shizuya, because they pointed out an attack which can break the original protocol proposed by Bagherzandi et al. Hasegawa et al. also showed how to enhance the protocol, and proved that the enhanced one is pparam-secure. In this paper, we prove that the enhanced one is PPSS-secure as well.
SUMMARYThis paper studies the complexity of computing discrete logarithms over algebraic tori. We show that the order certified version of the discrete logarithm problem over general finite fields (OCDL, in symbols) reduces to the discrete logarithm problem over algebraic tori (TDL, in symbols) with respect to the polynomial-time Turing reducibility. This reduction means that if the prime factorization can be computed in polynomial time, then TDL is equivalent to the discrete logarithm problem over general finite fields with respect to the Turing reducibility. key words: algebraic tori, order certified discrete logarithm, Turing reduction
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