Cryptographic pseudorandom generators (PRGs) can reduce the randomness complexity of computationally secure schemes. Nuida and Hanaoka (IEEE Trans. IT 2013) developed a security proof technique against computationally unbounded adversaries under the use of cryptographic PRGs. However, their proof assumed unproven hardness of the underlying problem for the cryptographic PRG. In the paper, we realize a fully unconditional security proof, by extending the previous result to “non-cryptographic” PRGs such as the one by Impagliazzo, Nisan andWigderson (STOC 1994) based on graph theory rather than one-way functions. In fact, our proof technique is effective only for some restricted class of schemes; then we also propose a “dual-mode” modification of the PRG to prove computational security even for schemes outside the class, while keeping the unconditional security for schemes in the class.