Security Level of Cryptography — Integer Factoring Problem
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Interpolation of Functions Related to the Integer Factoring Problem
The security of the RSA public key cryptosystem depends on the intractability of the integer factoring problem. This paper shall give some theoretical support to the assumption of hardness of this number theoretic problem. We obtain lower bounds on degree, weight, and additive complexity of polynomials interpolating functions related to the integer factoring problem, including Euler’s totient f...
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Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on fact...
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In 1984, Shamir [1] introduced the concept of an identity-based cryptosystem. In this system, each user needs to visit a key authentication center (KAC) and identify him self before joining a communication network. Once a user is accepted, the KAC will provide him with a secret key. In this way, if a user wants to communicate with others, he only needs to know the “identity” of his communicatio...
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Elliptic curves over the ring Z / n Z where R is the product of two large primes have first been proposed for public key cryptosystems in [4]. The security of this system is based on the integer factorization problem, but it is unknown whether breaking the system is equivalent to factoring. In this paper, we present a variant of this cryptosystem for which breaking the system is equivalent to f...
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The security of RSA depends critically on the inability of an adversary to compute private key from the public key. The problem of computing private key from public key is equivalent to the problem of factoring n into its prime factors. Therefore it is important for the RSA user to select prime numbers in such a way that the problem of factoring n is computationally infeasible for an adversary....
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