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12

This is standard mathematical notation and not specific to cryptography. The $\Pi$ symbol means Product in much the same sense $\Sigma$ means Sum. For instance, $$\prod_{i=0}^2{u_i^{m_i}} = u_0^{m_0}u_1^{m_1}u_2^{m_2}$$


10

In addition to the performance problems poncho already mentioned when using RSA signatures without hashing I just want to add on the security warning of poncho: Reordering If you have a message $m>N$ with $N$ being the RSA modulus, then you have to perform at least 2 RSA signatures as $m$ does not longer fit into $Z_N$. Let us assume that it requires ...


10

Yes, of course there is a benefit to signing unencrypted emails. The article you cite is solely about the combination of signature and encryption; it doesn't directly say anything about signing unencrypted emails. There is an important concern raised by the article which does apply to unencrypted emails, but that's because that concern applies equally ...


8

If you search on "timestamp", "timestamping", and "notary" on Crypto.SE and Security.SE, you'll find lots of references. I've collected a number of timestamping services that were mentioned in one of those places; this should provide a number of companies and online services you can check out: http://www.proofofexistence.com/ https://www.btproof.com/ ...


8

Yes. Modern cryptosystems are designed and analysed under the assumption that the key is never used for anything else. If you use your encryption keys for digital signatures, you are violating that assumption, and it is very easy to construct schemes where this violation will compromise security. It is possible to construct schemes that can use the same ...


8

The article you linked to predates the S/MIME 3.2 spec. If your client is sending S/MIME 3.2 messages, it should support header protection. Refer to RFC 5751 Section 3.1: In order to protect outer, non-content-related message header fields (for instance, the "Subject", "To", "From", and "Cc" fields), the sending client MAY wrap a full MIME message ...


6

No, signing the hash of the public key cannot introduce a weakness on a secure signature scheme. When we have a signature scheme, we assume that it is secure in an chosen text model, where the attacker has access to the public key, and can ask any text of his choosing to be signed. We can see that any such scheme (such as ECCDSA, or so we believe) cannot ...


6

Well, one reason to hash the data before signing it is because RSA can handle only so much data; we might want to sign messages longer than that. For example, suppose we are using a 2k RSA key; that means that the RSA operation can handle messages up to 2047 bits; or 255 bytes. We often want to sign messages longer than 255 bytes. By hashing the message ...


6

OpenPGP as defined by RFC 4880 knows two different encodings. Binary encoding Obviously, there is no reasonable limitation to an (ASCII) character subset in binary encoding. Radix 64 Radix 64 is also often entitled ASCII armored. In the end, it is a base64 encoding with a checksum. The content may consist of [a-zA-Y0-0+/=]. ASCII-armored OpenPGP ...


6

Because the RFC says so. Signing and verifying using this key format is done according to the Digital Signature Standard [FIPS-186-2] using the SHA-1 hash [FIPS-180-2]. It says the same for RSA half a page down. Apparently the signature algorithm is a defined part of the public key method's specification, rather than being negotiated ...


6

Short answer No, RSA encryption with a private key is not the same as RSA signature generation. RSA encryption can only be performed with an RSA public key according to the RSA standard. The terms Raw RSA or textbook RSA are often used to indicate RSA without a padding scheme. Raw RSA simply consists of modular exponentiation. Raw RSA is vulnerable to many ...


5

It mainly depends on how the algorithm was selected. If it was selected by a public competition like for AES, then it is likely to be secure. If it was forced in by the NSA such as Dual-EC random number generator, then you may have some doubts. Other questions you may want to ask yourself are: Is this an "original" algorithm or was the problem that it ...


5

I think you don't quite understand how RSA signatures work (and why they are the size they are). When generating an RSA signature, we follow a two-step process: We take that hash of the message we're signing, and convert (and pad) it into an integer $M$ which is between 0 and $N$ (where $N$ is a large integer that specified by the RSA key) We use the RSA ...


5

In a nutshell there are two main uses cases for signing an existing signature: validation: the signature of another person (ex: a superior) is required to give effect to a primary signature. The second signature covers the content, the first signature and potentially additional data added by the second signer. witness / notary: a second person signs only ...


5

Authentication can either mean entity authentication or data authentication. Data authentication is a means to demonstrate that some specific data originates from a specific source and has not been modified during transmission and/or upon storage. It can be achieved by the use of digital signatures in a public key, i.e., asymmetric, setting or message ...


5

Informally, a signature scheme with message recovery is one where some or all of the message is embedded in the signature, allowing to conserve bandwidth when transmitting a signed message, compared to a signature scheme with appendix. Total message recovery A signature scheme with total message recovery [some sources make total implicit, e.g. the HAC ...


4

No. Cryptography alone cannot solve this problem. Solving this problem requires a combination of technical (e.g., cryptography, systems security) and non-technical (e.g., legal, regulatory, contractual) solutions. Even the technical part is not solely a cryptography question; it as much about systems security.


4

Yes. An independent witness to the signing may vouch for the initial signing, and do so by signing the whole document. E.g. this could indicate that the signing was done by an officer of the company and not a rogue employee.


4

First of all I do not know your implementation, but it seems that you have some basic misunderstandings. Signature: ECDSA(sha256(Data) ) ECDSA is typically implemented in a way that you do not explicitly hash the data prior to passing it to the signing algorithm (but as this might be your own implementation and signing may still work correctly). ...


4

It depends on what you mean by RSA. If you mean the plain textbook RSA where $P = C^d \bmod n$ (decryption with private key $d$) and $S = M^d \bmod n$ (signature generation), then yes, they are the same. However, textbook RSA is inherently unsafe, and for real-life RSA such as RSA-OAEP+ (encryption) or RSA-PSS (signatures) signing is not the same as ...


4

Guillou and Quisquater (link) present a zero-knowledge proof of an RSA signature. Basically, the scheme is as follows: Public knowledge: RSA modulus $n$, public RSA exponent $v$, preimage $X$. Secret knowledge for prover: $A$, such that $A^v = X \mod n$. $$ \begin{matrix} \mathcal{P} & & \mathcal{V} \\ r \xleftarrow{\$} \mathbb{Z}_n^* ...


4

You can use multi-signatures. One example is the BN06 scheme described in the paper: Bellare, Neven - Multi-signatures in the plain public-Key model and a general forking lemma


4

SafeCurves lists some ways to compare the security of elliptic curves. Their security criteria are split to "ECDLP security" and "ECC security". Failing the former basically means "there is no way to use this curve securely in general" while the latter "it is difficult to implement this curve securely". None of the (few) BouncyCastle-supported curves that ...


4

The benefit to signing a non-encrypted email is that any recipient can verify that it was indeed you who wrote that non-encrypted email, unless your key was compromised (or the signing protocol has an exploit).


4

$q$ does not divide $s^e-h(m)$, but $p$ does, so since the gcd must divide both $s^e-h(m)$ and $n$ it's $p$. To be even more explicit, we know that $p$ divides both $s^e-h(m)$ and $n$. The only larger divisor of $n$ that is also divisible by $p$ is $n$ itself, but if $n$ would divide $s^e-h(m)$, then $q$ would also divide $s^e-h(m)$, which we already assumed ...


4

Yes, you can, but you would need access to raw or textbook RSA encryption and you would have to implement the PKCS#1 v1.5 or PSS padding primitives yourself. Beware that PKCS#1 v1.5 compatible padding is different for encryption signature generation. If you only have PKCS#1 v1.5 encryption or OAEP encryption available then the encryption routine will ...


4

Yes! (restrictions apply). ISO/IEC 9796-2 (scheme 1, SHA-1 hash, option 1 also know as implicit hash identifier, alternative signature production function) is a fully standard signature scheme, based on RSA, widely used in the Smart Card industry for public key certificates and message authentication, that adds only 22 bytes of signature overhead (if the ...


3

I am not quite sure if I exactly get what you are looking for, but I'll give it a try. This answer refers to the original question before the edit I'm looking for some kind of crypto-based data structure that will allow me to produce a signature over a set of hashes such that I can verify that any of the hashes is in the set at a later point in time ...


3

The standard definition of existential forgery allows the adversary to ask and obtain the signature of any message she wants, and claim success if she can exhibit (with sizable odds) any acceptable (message, signature) pair, for any message for which she did not ask signature. Update: There is also strong existential unforgeability, where the adversary ...


3

If you want $N$ serial numbers, your serial numbers will have to use $n$ bits for uniqueness, where $n = \log_2 N$. So if you have 100 bits to use for the serial, you could use 20 to get about a million serials and have 80 bits to use for a cryptographic MAC or signature. Now there are two approaches, the symmetric and the asymmetric. In the symmetric ...



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