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7

Thanks for the question! You are correct that there is a bug here. Indeed, the sentence "choose $\mathbf{b}_i$ s.t. $\ldots$" makes no sense: the LHS is in $H$, but the RHS may not be. Fortunately, there is a simple fix which guarantees $\mathbf{y}'_i \in H$. (This must have been what we intended in the first place, based on how the rest of the proof ...


4

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 ...


1

I am wondering why people are using RSA keys when some types of double substitution ciphers seem to be just as secure if not better off. First of all, RSA is an asymmetric cipher while a substitution cipher is a symmetric cipher. Asymmetric ciphers are used to achieve different security needs, e.g. TLS authentication or non-repudiation of documents. Or, ...


1

The simplest solution is to rely on identity-based signatures. A trusted third party (TTP) defines a set of RSA keys $\mathit{mpk} = \{N,e\}$ and $\mathit{msk} = \{p,q,d\}$ where $N = pq$ for two large primes $p,q$ and $e,d$ such that $e \cdot d \equiv 1 \pmod {(p-1)(q-1)}$. Key $\mathit{mpk}$ is public and is used to check the correctness of signatures; ...


1

Being able to validate the characters of a password independently is almost equivalent to storing the password in cleartext. If the password consists of $n$ characters in an alphabet of size $a$, then verifying hashed passwords requires $a^n$ queries. (A query is an online lookup until your password database is leaked, and a hash calculation after that.) ...


1

Validating individual letters of a password reduces complexity of guessing that password by trying all possible variants, so I would suggest avoiding such a design. PCP (probabilistic checkable proofs) is a well-known case of validating just a small portion of the "witness" (defined in that context), with focus on algorithm complexity. Regarding "1st ...


1

I believe the only way you can do this is to assume you have fixed length inputs to the hash function $f$. Otherwise, it is problematic what probability distribution you'd want to impose on the input set $\{0,1\}^{\ast}$ which is the collection of all finite input strings. In practice, hash functions do have an upper limit on the input string, but that's ...


1

To prove an encryption scheme to be perfectly secure, we need to prove: $$P[M=m|C=c]=P[M=m]$$ where $c$ is a cipher text and $m$ is a plain text. From Bayes theorem, we have: $$P[M=m|C=c]=\frac{P[C=c|M=m] \cdot P[M=m]}{P[C=c]}$$ It is noteworthy that: $$P[C=c|M=m]=P[K=k]$$ where $K$ is the key space and $k$ is a particular key. Now: ...


1

So, I does anybody know how to design a module for remainder operation in >verilog that computes the remainder in a single clock cycle? Any links to >literature discussing the algorithm would suffice. A nieve implementation would be something like. parameter bitwidth; input [bitwidth-1:0] a; input [bitwidth-1:0] b; output reg [bitwidth-1:0] result; reg ...



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