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A proof of a linear combination lemma on \(\mathbb{Z}_m\). (Chinese. English summary) Zbl 0923.11168

Authors’ abstract: The paper gives a proof of a linear combination lemma on \(\mathbb{Z}_m\), i.e., the discrete random variable \(Z\) is independent of the \(k\) independent random variables \(Y_1,\dots,Y_k\) if and only if \(Z\) is independent of the sum \(c_1Y_1+\cdots +c_kY_k\) for very choice of \(c_1, \dots, c_k\), not all zero and \(\text{gcd}(\text{gcd}(c_1, \dots,c_k),m) =1\).

MSC:

11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94A60 Cryptography
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