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Since a single computationally hard problem today may possibly be solved efficiently in the future, many researchers endeavored in recent years to base their cryptosystem security on solving two or more hard problems simultaneously to enhance the system security. However, it is found that many previously suggested signature schemes with their: security based on integer factorization and discrete logarithm problems and with; verification equation using exponential quadratic forms were not as secure as claimed and gave no provable security under the random oracle model.
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