Jalaj
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 Jan 27 comment RS Erasure Coding and Shamir's Secret Sharing I am not sure if any erasure code can be used to construct a secret sharing scheme. I would definitely like to see a reduction in that scenario. Reed Solomon has a direct relation with Secret Sharing if we see the space of all messages as the secret space and therefore, we have the bound. It is possibly for BCH also to show secret sharing property for the multivariate generalizations of Shamir-Secret sharing, but how to argue for codes, say like Reed Muller code or even Hamming code! Jan 27 answered Current mathematics theory used in cryptography/coding theory Jan 27 comment Current mathematics theory used in cryptography/coding theory Lattice based systems can be seen as a special form of coding theory scheme. For example, LWE can be seen as perturbation of a code word in a proper finite field. Jan 27 revised RS Erasure Coding and Shamir's Secret Sharing added 3 characters in body Jan 27 answered RS Erasure Coding and Shamir's Secret Sharing Jan 27 revised Designing a key expander out of ciphers deleted 10 characters in body Jan 27 comment Designing a key expander out of ciphers My idea is to use the same resilient function to encrypt as well. Since the output of the resilient function is uniform even if $n-1$ input are fixed, we can use $y$ as one of the uniformly randomly picked value and rest of the value some fixed $IV$, just like hash function. Once we do this, we get two random values. We can use a $n,1,n-2$ or the same old resilient function with $y$ and last iteration output as the randomly chosen input and rest as $IV$ and so on. The resilient function is a public knowledge, so it can act as the encryption scheme. I see it is like iterated hash function! Jan 26 revised Designing a key expander out of ciphers added 8 characters in body Jan 26 comment Designing a key expander out of ciphers You reformulated the question like that. Alice is given $n$ ciphertexts, one of them is secure, and hence the corresponding encryption scheme satisfies the indistinguishability definition of the security, hence the output of that encryption scheme is uniform, giving me the $1$ variable to construct the $n-1$ resilient function. Once $y$ is computed, Alice keeps on re-encrypting $y$ using the key, $k$, $i+1$ times to get $i^{th}$ key. Now on the part of Bob, since he knows $k$, he can generate the keys in decrypting the $n^{th}$ encryption that corresponds to $n^{th}$ key and so on. Jan 26 answered Designing a key expander out of ciphers Jan 26 revised Provable Encryption added 12 characters in body Jan 26 answered Provable Encryption Jan 26 answered How can I repeatedly prove I have data another has seen without sending the data and without the other storing the data? Jan 25 comment How to construct encrypted functions (with either public or private data)? I am glad that I was able to clear my remarks. Actually, I had a discussion with Vinod when he was visiting my university last term on the history of FHE and its application. I remember him citing evoting, private function evaluation, $\mathsf{CRHF}$, and $\mathsf{PIR}$ as pure applications of FHE or rather put in his words, "the holy grail of cryptography!" Jan 25 answered Stretching a random seed to maximize entropy Jan 23 comment How to construct encrypted functions (with either public or private data)? I am talking about "motivation" and why people cared about FHE. All other applications are just a bonus. I can cite thousands of examples. Another famous example is one-way function. They were motivated to do cryptographic task, but they are one of the key ingredients in proving many complexity-theoretic results as well. In fact, their explicit existence will resolve the famous $\mathsf{P}$ Vs $\mathsf{NP}$ problem! But this, by no means suggest that OWF was coined to prove $\mathsf{P} \neq \mathsf{NP}$. This would be plain wrong. Natural proofs and Relativatization were done for that purpose. Jan 23 comment How to construct encrypted functions (with either public or private data)? I went through Section that you mentioned. It clearly says, "With FHE, some functions can be evaluated privately" and this is exactly what I mentioned in my comment. You may evaluate private function using FHE, but FHE was not motivated to do this. The paper I mentioned does exactly the same! Primitives are developed and their applications are found later on. For example, PSG are used to construct randomness extractor, but well, PRG was not developed to do that task: the prime motivation of PRG was to derandomize $\mathsf{BPP}$. There are many such examples. Jan 23 awarded Commentator Jan 23 comment How to construct encrypted functions (with either public or private data)? I just read the abstract and the first page of the introduction. This paper also concerns with only performing some circuit operation (publicly known) on encrypted data. It does not perform publicly known data on private circuit. It does not say that the motivation of constructing a FHE is to compute private functions. The prime motivation was to compute public function on encrypted data. Jan 21 comment How to construct encrypted functions (with either public or private data)? You may require homomorphic encryption to do the task, but homomorphic encryption is not constructed to perform the task. For example, Mohassel had a paper in CANS 2011 titled "Fast Computation on Encrypted Polynomials and Applications" which if I remember correctly performs the task of evaluation of encrypted polynomial by using additive homomorphic encryption scheme. You can find work on this line, but sure enough, homomorphic encryption is devised to evaluate a publicly known circuit on encrypted data, nothing more than that!