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You should not use keys smaller than 1024, and even 1024 is considered too small today. However, if you want additive homomorphism, then you can you encrypt with "ElGamal in the exponent" over Elliptic curves. To explain what I mean by this, let $G$ be the base point (generator) for the Elliptic curve group, let $x$ be the ElGamal private key, and let ...


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In order to answer this question, we need to understand the basis behind all of modern cryptography, which is computational hardness. Today, we believe that we know how to construct block ciphers that are secure, except for brute force search (or almost that secure). However, we don't really know this. We also think that factoring is hard, and so on. All of ...


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Big numbers must be better than small numbers right. That is the logic behind those kinds of claims. The reality however is computing is limited to the laws of the physical universe. Setting quantum computing aside for now, the complexity of a problem can be translated into an energy cost. For classical computing that means that 128 bit is "beyond brute ...



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