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7

I don't think idea 1 can be made to work at all. The main point is that in order to generate a correct secret decryption key, the key generator must know the order of $\mathbb Z^*_n$, i.e., the totient of the modulus $n$. The generator knows that $n=p \cdot q$, where it believes that $p$ and $q$ are primes, and so it believes that the totient is ...


4

As long as you're using any modern encryption algorithm (and you're using it correctly: random key, new random or unique IVs for each message, depending on the mode of operation, etc.) then you'll be fine. In fact, you'd be fine even if an attacker got to choose which plaintext you encrypted and got to see the result; this information would not help him ...


3

I am wondering if using Skein or the Keccak hash algorithm in this construction (as a stream cipher) is secure: In the case of Skein and Keccak it should be secure. However, both of those have defined their own cipher modes which you should IMO prefer. (For compatibility, if not security.) The Skein one is defined in section 4.10 of the paper. It uses ...


3

Chris's answer is great. As it does not address how one would detect #2, I'll take a stab at it. Assume there is some watchdog looking at public keys in your system, trying to detect a problem. They can easily tell if two public keys share a prime by computing gcd. A gcd of anything other than 1 would identify bad keys. So, let's assume that once two ...


3

The most effective trapdoor I could imagine an adversary building into an RSA key generation algorithm would be the following: Preparation The adversary generates a set of RSA keys of varying sizes. The public keys will be built into the malicious key generation code, the secret keys are kept by the adversary. Key generation algorithm The algorithm is ...


1

The other answers tackle 2. very well, so I'll only look at 1. I think it can be made to work in some specific instances, namely if the key generator was part of a closed product with its own key storage or the private key used a format where only the modulus and exponents were stored. (Note that 2. is not common, because knowing the primes can be used ...


1

If you replace $H$ with a MAC that is build using $H$, i.e. NMAC, then it will be provably secure. Encryption will be $C_i = MAC_k(IV | i) \oplus P_i$. You are guaranteed by the MAC security property (existential forgery) that an adversary cannot generate any of the key stream on his own and so you are left with a secure stream cipher. Just using $H$ by ...



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