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Abstract: In this paper, we discuss coding theorems on a $2, 2$-threshold scheme inthe presence of an opponent who impersonates one of the two shareholders in anasymptotic setup. We consider a situation where $n$ secrets $S^n$ from amemoryless source is blockwisely encoded to two shares and the two shares aredecoded to $S^n$ with permitting negligible decoding error. We introducecorrelation level of the two shares and characterize the minimum attainablerates of the shares and a uniform random number for realizing a $2,2$-threshold scheme that is secure against the impersonation attack by anopponent. It is shown that, if the correlation level between the two sharesequals to an $\ell \ge 0$, the minimum attainable rates coincide with$HS+\ell$, where $HS$ denotes the entropy of the source, and the maximumattainable exponent of the success probability of the impersonation attackequals to $\ell$. We also give a simple construction of an encoder and adecoder using an ordinary $2,2$-threshold scheme where the two shares arecorrelated and attains all the bounds.



Autor: Mitsugu Iwamoto, Hiroki Koga, Hirosuke Yamamoto

Fuente: https://arxiv.org/



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