# Tag Info

4

Each additional signature halves the security level. A security level of about 64 bits can be broken by a determined attacker, and a level of 32 bits can be trivially broken on a single home computer. So if you use 256 pairs, which is a reasonable level, since it offers 256 bit security against second-preimage attacks, and 128 bits against collisions, ...

4

If he chooses $s$ at random, then the scheme will be stateless but will fail after using the same $s$ twice, which should happen after giving approximately $\:$$\Theta$$\big(\hspace{-0.05 in}$ $2^{H/2}$$\hspace{-0.01 in}\big)\:$ signatures. If he chooses $s$ by applying a PRF to $g(m)$, then the scheme will be deterministic and stateless, but can be ...

4

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 ...

3

HMAC nor a KDF is needed here. As long as you always use a constant size key and "tag" (generally called a nonce, as in number-used-once) you can simply use a secure hash function, like SHA-256. My suggestion is to drop keeping track of the tags sent so far - this administration is bound to fail at some point. Instead, generate a 32 byte random number. This ...

3

Yes, it makes sense to truncate the hash to 128 bits. The security proof actually says that if finding a preimage for F requires effort 2^n, then breaking the Lamport signature scheme with G having k-bit digests requires effort (2^n)/(2k). So strictly speaking, with F truncated to 128 bits and G having 256 bits (2k=512=2^9), you will have 128-9=119 bits of ...

3

The only requirement is $i,b \neq i^*,b^*$ where $i^*$ is a random value from $1$ to $l$ and $b^* \gets\{0,1\}$ So if $b^*=0$ then $b=1$. Don't get confused by the $x$, it has nothing to do with the secret key, it's just a variable that later becomes $y_{i,b}=f(x_{i,b})$. It could as well be called $a$.

3

Keyed hashing is usually used to build message authentication codes (MACs), the most common of which is the hashed-based MAC (HMAC). MACs are basically cryptographic checksums. They are used to detect when an attacker has tampered with a message. Therefore they require a secret key (to be withheld from an attacker) and should be as fast as possible (to ...

3

You've stumbled on the requirement for authentication. Recall that signature schemes have a private key and a public key. The private key is used to sign the document in question, and the public key is given to the verifying party so that they can verify that the signature is correct. You're correct that it is possible to strip a digital signature and ...

3

Well, $f$ is assumed to be a one-way function. That means, there cannot exist an efficient algorithm for finding preimages under $f$. The algorithm $A'$ is what we call a reduction. We are trying to show that an efficient algorithm for attacking the signature scheme does not exist. To do that, we assume the contrary, i.e. we assume an efficient algorithm ...

2

This is the algorithm from your other question Lamport-Diffie + Security Proof , I guess. What happens here is this: We create a special public and secret key for a LD-Sign Scheme: We choose $x_{i,b}$ randomly for all but one single entry (which is $x_{i^*,b^*}$) and this is our secret key. In the public key we just apply $f(x)$ to all randomly chosen ...

2

$w$ is a parameter that can be freely chosen, to maximize performance. Each element of the signature encodes $w$ bits of the message to be signed, so the larger $w$ is, the fewer elements you need to include in the signature. If you make $w$ large, then signatures can be shorter; however, the tradeoff is that key generation, signing, and verification run ...

2

The security of the LD scheme can be reduced to the one-wayness (aka preimage resistance) of the used hash function. The reduction is quite easy: Assume you want to invert the one-way function $f$ for image $y=f(x)$, given a forger for LD-OTS. Then you generate a valid LD key pair using $f$, sample a random position i in the key pair and a bit b and ...

2

For any signature scheme, we can remove a few bits of the signature, say $k$, and define a verification scheme that accepts the signature if any of the possible $2^k$ original signatures matching the truncated signature is acceptable. The risk of forgery is increased by at most $2^k$ but might remain acceptable. The work to verify the signature is increased ...

2

It is not only a good idea to choose independent and fresh randomness for every signature, it is (as Alex mentioned in his comment) necessary, as otherwise anyone who gets two signatures of you computed with same randomness for different messages can extract the private signing key with overwhelming probability. I'm using the notation from the Wikipedia ...

2

In the blind RSA signature scheme the blinding of a message $m$ (to be blindly signed) is multiplicative with value $r^e$, where you ensure that $r$ is invertible modulo $N$. So if the sender receives the signed blinded message back from the signer, he can unblind by multiplying with $r^{-1}$, yielding $s\equiv m^d \pmod N$ which is a valid (textbook) RSA ...

2

The answer is "any sane summarization function is about as good as any other; pick whichever is convenient" To the best of our knowledge, SHA-256 acts pretty much like a random function (except for the length extension attack; that wouldn't apply here) So, the output of SHA-256 is essentially a random 256 bit number; so, if we have a 128 bit hash function: ...

2

As D.W. notes, this works for the purpose in question. Actually, relying on number theoretic assumptions for the accumulators will give you no benefit as you have observed. However, here is a construction of accumulators from Nyberg in FSE'96, which does not rely on number theoretic or any computational assumptions. This is the paper of Nyberg and you may ...

1

Ed25519 or more general the EdDSA (Edwards-curve Digital Signature Algorithm) approach can be considered as a variant of ElGamal signatures (such as Schnorr or DSA). They all are signatures following the hash-then-sign approach. This simply means that you can sign arbitrary length messages by hashing them to a constant size string using a secure ...

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As I already outlined in this answer, hash trees in combination with any one-time signature scheme gives the so called Merkle signature scheme. I assume there is some misunderstanding and therefore I sketch merkle signatures subsequently: The idea is to produce $n$ key pairs $(X_i,Y_i)$ of a one-time signature scheme and then to take the hash values ...

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The main difference is that the salt is not assumed unknown to the attacker, but the key is. An additional difference is that salts are supposed to vary; if you hash three passwords within the same system, then you should use three distinct salt values, whereas keys are reused. Another way of seeing salts is to consider that you do not have one hash ...

1

What do you mean by forge? If you are asking about (the common) existential forgery, then two message, signature pairs are enough, given that the messages differ in at least two bits. As an example consider that you have the signatures for $m_1 = 1111$ and $m_2 = 1100$. Considering the preimages you now have, you can forge signatures for $m_3=1101$ and ...

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