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This is a) no attack on the security model, but an attack in the security model of EUF-CMA, and b) a generic attack on any signature scheme that signs the hash of a message instead of the message itself (as done in RSA-FDH). The idea is that if you can find a collision for the used hash function $H$, i.e., two messages $m_1, m_2$ such that $H(m_1) = H(... 3 HMAC (and any other MAC) are totally different from Digital Signatures (RSA, DSA, ECDSA, EdDSA). MACs require a shared secret key that both the communicating parties have. The same secret is used to create the MAC as is used to verify it. Anyone with the shared secret key can create a MAC, and anyone with the shared secret key can verify a MAC. Digital ... 3 Your understanding is correct. PKI would be the service that verifies that Bob's public key really belongs to someone named "Bob". As long as Alice trusts the certificate authority that certified Bob's public key, she can implicitly trust that the public key she sees really is Bob's, not Eve performing a MITM. The internet is secured with web PKI, which is ... 3 Suppose you have two message signature pairs and following values are then public i.e. known to you - The public keys:$Q_1 (= x_1G)$,$Q_2 (= x_2G)$The messages and their hashes:$m_1$,$m_2$,$H(m_1)$,$H(m_2)$The signatures:$(r_1, s_1)$, ($r_2, s_2$) The following are unknown - The private keys:$x_1$,$x_2$The nonce:$k$The following relations ... 2 To give an example with less maths, suppose that I come to you and ask you to sign the message "Josiah's favourite number is 747895723190543. Weird I know." You think that is a bit odd, but harmless so you do so. Unbeknown to you, the hash of that message is also the hash of "Please pay Josiah the sum of 87476 United States dollars." Because the hash ... 2 The certificate is much more than a public key, changing the public key will of course prevent verification but most of what you did doesn't change that. Your certificate above also has the following information: Common Name: INNOPAY Organization: INNOPAY BV Organization Unit: Fun Department Locality: Amsterdam Country: NL Valid From: July 24, 2019 Valid To: ... 2 Cryptographic sealing is the application of asymmetric cryptography to encrypt a session key so that it cannot be used-- until it is decided to remove the seal and use the key. It is a protection mechanism. See this description from Oracle: Sealing the symmetric key involves creating a sealed object that uses an asymmetric cipher to seal (encrypt) the ... 2 Is there a risk when publishing multiple signature for the same message ? As long as the keys are independently generated, there's no risk. This simply follows from the fact that every forgery on the composite scheme - the message signed with$n$different keys / signature schemes - immediately implies a forgery against at least one of underlying signature ... 1 When you exponentiate a number$x$modulo$n$to the$i$-th power, as you increase$i$, you will eventually reach$x$again. In your example,$89^{3017} \pmod{3127} = 89$. This "magic exponent" is computed as$\phi(n) + 1 = (p-1)(q-1) + 1$. This is Euler's Theorem, see the Wikipedia article for a proof. In RSA, we choose the numbers$e$and$d$such that, ... 1 Which of the hash versions (hash_bin – 4 bytes / hash_text – 8 bytes) is better to use for signing the hash by RSA, security-wise? Doesn't matter; as long as there is a 1:1 relationship between versions, it doesn't matter which representation you sign. The only situation where you might run into a problem is if two different hashes (with version A) mapped ... 1 Signed Prekey is one of the long-term prekeys which is used in X3DH. The public component of Signed Prekey is signed by the Identity private key and sent to the Key Distribution Server as part of key bundle. To make sure that the server doesn't tamper with key bundle, Signed Prekey is signed by the Identity key and Identity key is verified using out of band ... 1 A valid signature$\sigma$satisfies the very special property that$\textsf{Ver}(vk,m,\sigma)=1$, whereas a random value$\tilde \sigma$will surely not satisfy this property. So a signature simply cannot be indistinguishable from random if$vk$and$m$are known. And if you consider$vk$or$m\$ to be secret, then you are leaving the standard realm of ...