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1

The binary base 64 encoded blob contains a modulus which is 257 bytes in size: ...

2

It will be uniformly random for such a simple statistical test. The problem is that you are treating the probability of bits having a particular state as independent of each other. You would need to look at the conditional probability distributions of certain bits being set given other bits. The entire joint distribution of output and input bits for a ...

5

There is some confusion here. The definition of prime numbers states that cannot be factored (see Definition of prime numbers) You seem to be talking about RSA modulus which is the product of two prime numbers (see RSA cryptosystem). As far as keylength is concerned 768 bits is not considered safe today. Note that the keylength choice is a compromise ...

4

OK, so this takes a bit of guessing, but I'm assuming the following: A is the identity of A, which can be used to select the right public key of A; Kxa() is a signing operation (with message recovery) that signs the random Ra and a tag Ts which is used as proof; Kya() is an encryption operation with the public key A, so that the session key Ks is kept ...

4

Another solution (cf to @Raoul722 comment) is the following: It is easily feasible with a mix of symmetric and asymmetric encryption. Assume each user $k$ have a key pair: $(K_{pub}^k,K_{priv}^k)$. The admin also have his key pair: $(K_{pub}^{admin},K_{priv}^{admin})$ where $K_{pub}^{admin}$ is known by all. Encryption scheme for a user $k$: generate a ...

5

It depends on the block cipher in question - specifically its key schedule. Knowing any round key of AES-128 would let you calculate the key, because the schedule is reversible. OTOH, e.g. TEA would retain secrecy of most of the key and might remain secure, because its round keys are small enough parts of the key. In the case of DES, it is weak enough to be ...

-2

The only inevitable data dependence in Base 64 encoding or decoding is on the length of the value being encoded or decoded. Encoding Extraction of 6-bit value by bit shift and masking: constant time. Conversion from 6-bit to a character: indexing into a 64-character table, constant time. Decoding Conversion from a character into a 6-bit value: ...

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