Eugen

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Mar 22	awarded	Student
Mar 18	accepted	How to verify a number encrypted with an unknown key
Mar 18	comment	How to verify a number encrypted with an unknown key @antosecret This kind of scenario could be useful when fine grained data must be known only to Alice (e.g. 40, 45, 18, etc..) but the aggregated information is ok to share with Bob (e.g. their sum). Alice could give her secret key for Bob to decrypt the sum but this would enable him also to decrypt the terms. Note that Bob takes the computation overhead by "summing" the terms in encrypted form, he only asks Alice to tell what that number is but would like to verify she is not lying.
Mar 18	comment	How to verify a number encrypted with an unknown key @DavidSchwartz The scheme is not that simple. When Alice stores data, she stores the terms (e.g. 40, 45, 18, etc.) encrypted with her secret key. The terms are then added by Bob, at some later time. So Bob would obtain 40+45+18=103 in encrypted form. 103 is encrypted with Alice's secret key. So Bob needs to ask her to decrypt the value and send it (in my case re-encrypted with Bob's key, but this is not essential). The question is how to verify Alice indeed sends the correct sum and not 103-20 = 80 for example.
Mar 18	comment	How to verify a number encrypted with an unknown key @RickyDemer You are right.
Mar 18	revised	How to verify a number encrypted with an unknown key added 6 characters in body
Mar 18	comment	How to verify a number encrypted with an unknown key @DavidSchwartz Bob doesn't know. The Paillier crypto-sytem is such that by multiplying the ciphertexts you obtain the sum of the plaintexts in encrypted form.
Mar 18	asked	How to verify a number encrypted with an unknown key
Feb 6	comment	Is such a crypto-system available? @poncho Regarding the storage you are right: its either storing or recomputing it every time you need to retrieve/share some data. Making new trees requires recomputing not only the hashes but re-encrypting the database on each insertion :). I hope it is understood that this is just an open discussion. I am not nitpicking or something like that.
Feb 6	comment	Is such a crypto-system available? @poncho Could you point out to a paper that explains the efficiency of the factorization in case same modulus is reused for multiple pairs?
Feb 6	comment	Is such a crypto-system available? @poncho The solution satisfies the requirements although I would like to share my thoughts on its deficiencies (btw. Bob knows k_new and Eve knows k2). First is the storage overhead needed to store the hash tree. With the Barack Obama's solution I have to store k_new (and modulus) only for the portions I share (although public key crypto is much slower than symmetric encryption). If new data is added there is a problem again (if I shared H8 now Bob would know also H16, H17, right?). Regarding my interests: they are mixed indeed, but solving the real example has a bigger priority for me.
Feb 6	awarded	Commentator
Feb 6	comment	Is such a crypto-system available? @BarackObama I think the conditions haven't changed that much from the original (a non-negligible change is that I haven't thought that alternative k2' k_new' pairs might reveal original k1). The use case description is just an example to help other readers understand the abstract description, no new requirements are introduced there. However it may be, I am thankful to all people considering this post worth spending their time, regardless of the actual contributions. By the way using different modulus for different pairs seems to solve the (k2', k_new') problem.
Feb 6	awarded	Scholar
Feb 6	accepted	Is such a crypto-system available?
Feb 6	revised	Is such a crypto-system available? added 12 characters in body
Feb 6	comment	Is such a crypto-system available? @fgrieu there is no need in a trusted authority. Alice generated k1, k2 and computes k_new as a function of k1 and k2. It is ok if k_new is independent of k1 and k2 but I can't imagine something like this is possible (after all c2 is some sort of a function of k1 and k2). Bob needs only k_new to recover the original plaintext.
Feb 6	comment	Is such a crypto-system available? @IlmariKaronen yes the questions seem to be identical, except mine has a "non-theoretical" use case :) and there is no requirement on the type of cryto-system used.
Feb 6	revised	Is such a crypto-system available? added a use case
Feb 6	comment	Is such a crypto-system available? It doesn't matter for me as long as it satisfies the properties specified in the question. The originator of the data has key k1, Alice has key k_new. Even if Alice finds k2 or any other pairs (k2', k_new') she shouldn't be able to compute k1.