| Project/Area Number |
10680330
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | Tohoku University |
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Principal Investigator |
SHIZUYA Hiroki Education Center for Information Processing, Tohoku University, Professor, 情報処理教育センター, 教授 (50196383)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥300,000 (Direct Cost: ¥300,000)
Fiscal Year 1998: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | encryption function / one-way function / reducibility / semantic security / discrete logarithm / integer factoring / bounded arithmetic / ハードコア述語 |
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| Research Abstract |
Let f be a one-to-one encryption function. Given f(m) and a string K, can we efficiently determine whether m contains K as a substring or not? We investigated the computational complexity of this problem. Our main results show that for an injective one-way function f, the following three functions are equivalent with respect to the polynomial-time Turing reducibility.
1. The function that on input f(m) and a string K, outputs 1 if m contains K; 0 otherwise.
2. The function that on input f(m) and a string K, outputs the number of K contained as substrings in m.
3. fィイD1-1ィエD1, I.e. the inverse function of f.
This implies that searching a plaintext for the key word without decryption cannot by completed in polynomial-time if f is really one-way. Under the same assumption, we cannot count in polynomial-time how many times the key word appears in the plaintext.
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