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This paper introduces two new public key encryption techniques namely the "logarithmic-factorized (LF)" and the "double-exponentiation (DE)" cryptosystems. The main one-way trapdoor functions of these algorithms are the general form of the generalized discrete logarithm problem (GDLP), the integer factorization problem (IFP) and the double IFP (DIFP). The LF algorithm depends simultaneously on both the GDLP and the IFP, while the DE algorithm depends on the DIFP. The validity of these algorithms is proven by applying them to messages and returning the original messages in various numerical examples. The proposed cryptosystems have many advantages that are explained in detail.