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7

There is a method known as "Complex Multiplication". However, it is not simple at all, and tends to be overly expensive for most target orders. See this article for some details. There is also the (theoretical) concern that a curve constructed that way may have a special structure though could possibly be leveraged into an attack one day; generally speaking, ...


6

Yes, the basic idea of hardcoding a public key is secure. It is sometimes recommended as an alternative to the complexity TLS and PKI bring – otherwise it can be easy to skip a crucial step and end up with little or no security. However, the "encrypt a secret for server" scheme has some weaknesses compared to TLS. The clearest is lack of forward secrecy ...


4

Yes, (asymmetric) encrypt-then-sign would provide the same properties as (symmetric) encrypt-then-mac. It would provide integrity and authenticity of the ciphertext. It is however possible for another person to re-sign the encrypted message if encrypt-then-sign is used. This is a problem when other parties are trusted within the same network. Note as well ...


3

I will give you the simplified answer. The public key encryption does not prevent adversery from computing private key from public key. It just makes it very very very hard. The algorithms use math that allows simple private->public calculation, but public->private has no good mathematical "shortcuts". It would take adversery more time to calculate this, ...


3

Is there some safe way to sign the private key used for encryption with the signing keys? What you're talking about is also commonly referred to as "keychain" or "keyrings", a concept popularized by programs like GPG, which do exactly this: They generate one master signature key, which you securely distribute and which then "certifies" the other ...


2

Basically RSA signatures work just like encryption but with the keys exchanged. If somebody tells you $m^{sk}$ you can easily test if $$ (m^{sk})^{pk} \equiv m\ (mod\ N) $$ but you cannot calculate $m^{sk}$ yourself. The problem/trick is the usual, exponentiation is easy but logarithm is hard. (I like using $sk$/$pk$ for secret-/public-key rather than ...


1

There can be much simpler methods than CM for group orders of a specific form. For exemple if $p \equiv 2 \pmod 3$ and $b \not\equiv 0 \pmod p$, the curve $Y^2 = X^3 + b$ over $\mathbf{F}_p$ has $p+1$ points. (The proof of this is easy and left as an exercise.) Such methods are also used to easily construct "good enough" pairing-friendly curves. As Thomas ...


1

Regarding the 3rd part of your question, "Can and should ordinary, run of the mill elections be conducted online ..." - If one thinks of an election as a problem around the issue of preserving the privacy of many inputs (a people or population's votes) while correctly producing the right result (i.e. correctly tabulating the outcome of the election) and ...


1

As far as I know, unknow key-share (UKS) attacks are mostly related to key exchange protocols. Presentation An UKS attack on an authenticated key exchange (AKE) protocol is an attack whereby an entity $A$ ends up believing he shares a key with entity $B$,and although this is in fact the case, $B$ mistakenly believes the key is instead shared with an ...


1

Ok, suppose that we have a ciphertext $(c_1, c_2, ..., c_8)$ that we wish to decrypt. What we start off with is to make a guess for $p_8$, which is the decryption of the last byte of the block. Suppose that we guess that it is 0x07; we then need to validate that guess. What we do is create a two block message; the second block is the challenge ciphertext ...



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