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I want to create the parameters for a bilinear pairing (the Tate pairing in this case). In case you're interested I'm following this thesis, http://crypto.stanford.edu/pbc/thesis.pdf, specifically the type F curves (page 61) which has embedding degree k = 12. But it's probably not necessary to refer to the thesis to...
When encrypting with RSA one would do the following: m^e % n Where `m` is what we encrypt. Often e is a very big number to make it more difficult to crack. So how does one avoid overflow when encrypting?
Does the encryption with a private key and decryption with a public key works in ElGamal likewise what is done when we use RSA for sender authentication?
I want to create the parameters for a bilinear pairing (the Tate pairing in this case). In case you're interested I'm following [this thesis](http://crypto.stanford.edu/pbc/thesis.pdf), specifically the type $F$ curves (page 61) which has embedding degree $k = 12$. But it's probably not necessary to refer to the the...
I am trying to implement El Gamal in java without using the in-built libraries. The problem occurs when I am trying to find the generators of the number(in this case 11). Everything works perfectly except that it is returns 10 as a valid generator of 11(which it is not, right?) public void generateKey() ...
How can I prove the following : "if f is a one-way function, then it is an uninvertible function" ??
I am trying to implement El Gamal in java without using the in-built libraries. The problem occurs when I am trying to find the generators of the number(in this case 11). Everything works perfectly except that it is returns 10 as a valid generator of 11(which it is not, right?) public void generateKey() ...
I have a program (a game) that uses Java's `nextInt` function with parameter 0x10000 to get a random 16-bit number. Java's `nextInt()` is an 48-bit seed LCG with the following formula: seed[n+1] = (seed[n] * 0x5DEECE66DL + 0xB) mod (1 << 48) `nextInt()` is implemented in such a way that the random number ...
I have a program (a game) that uses Java's `nextInt` function with parameter 0x10000 to get a random 16-bit number. Java's `nextInt()` is an 48-bit seed LCG with the following formula: seed[n+1] = (seed[n] * 0x5DEECE66DL + 0xB) mod (1 << 48) `nextInt()` is implemented in such a way that the random number ...
> Would we also need some additional options/messages in GnuPG to make it clear when you might be looking at an "unauthenticated" signature? OpenPGP does not trust keys simply because lots of people have signed them. You must "set ownertrust" for the keys you have before they will be used in Web of Trust calculation...
> Would we also need some additional options/messages in GnuPG to make it clear when you might be looking at an "unauthenticated" signature? Hopefully I'm not stating the obvious. OpenPGP does not trust keys simply because lots of people have signed them. You must "set ownertrust" for the keys you have before the...
> Would we also need some additional options/messages in GnuPG to make it clear when you might be looking at an "unauthenticated" signature? Hopefully I'm not stating the obvious. OpenPGP does not trust keys simply because lots of people have signed them. You must "set ownertrust" for the keys you have before the...
I'm a user of Zeo too, and had the same problem with an encrypted data file. I found this question, but it appears to be unanswered. So I took another obvious path of social engineering instead. Searched around and did blind contact with some of the former members of Zeo to see if I could talk them into releasing ...
When encrypting with RSA one calculates $ m^e \pmod n $ by doing the following: m^e % n Where $m$ is what we encrypt. Often $e$ is a very big number to make it more difficult to crack. **So how does one avoid overflow when encrypting?**
I'm a user of Zeo too, and had the same problem with an encrypted data file. I found this question, but it appears to be unanswered. So I took another obvious path of social engineering instead. Searched around and did blind contact with some of the former members of Zeo to see if I could talk them into releasing ...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
How do we analyze the security of a compression function in the secret key model? More formally, let $H$ be a hash function and $F(IV,M)$ its compression function. Suppose we generate a MAC as follows $$ T=F(F(K,M),M_p), $$ where $K$ is the MAC key and $M_p$ is the padded block. Can I say that if one observes the...
I need to find a secret sharing scheme with these properties: - The scheme is set up by all participants, ie no single entity called the dealer - The parameters of secret sharing need to be modifiable,eg enrollment, disenrollment, change of access structure, ... - Need to be verifiable, ie participants could c...
A message is sent from a person to another. The plain message is first encrypted, even with a weak algorithm - say, DES. Then, the encrypted message is encoded with a simple substitution, which is private and remains the same through all the conversation. Is it feasible for an external attacker to decrypt the messa...
Is it feasible to break an encrypted and later encoded message?
One-way in the context of cryptography is usually defined to mean that, given an element from the range of a function (or even a series of elements from the range), it is not possible in time polynomial in the input (or maybe output) size to identify the element(s) in the domain that yields the range element(s). This ...
One-way in the context of cryptography is usually defined to mean that, given an element from the range of a function (or even a series of elements from the range), it is not possible in time polynomial in the input (or maybe output) size to identify the element(s) in the domain that yields the range element(s). This ...
According to the birthday paradox we need approximately $O(|T|^{1/2})$ samples from the tag-space to find a collision for a hash function $h:K\times M \to T$. But how many samples are needed to find a three-way collision, i.e. $h(a) = h(b) = h(c)$ for three messages $a,b,c \in M$ hashed with the same key $k\in K$ ? ...
According to the birthday paradox we need approximately $O(|T|^{1/2})$ samples from the tag-space to find a collision for a hash function $h:K\times M \to T$. But how many samples are needed to find a three-way collision, i.e. $h(a) = h(b) = h(c)$ for three messages $a,b,c \in M$ hashed with the same key $k\in K$ ? ...
What is the padding scheme for the original Tiger hash?
I have the following problem: Alice wants to send Bob a message such that Bob knows it is from Alice but at the same time he cannot prove that Alice send him this message. The solution I came up with is: 1. Alice picks a random key K, and encrypts the message M to M'. 2. Alice encrypts K using Bob's public key,...
I have the following problem: Alice wants to send Bob a message such that Bob knows it is from Alice but at the same time he cannot prove that Alice send him this message. The solution I came up with, using RSA, is: 1. Alice picks a random key K, and encrypts the message M using this key K. M'= aes(K, M) 2. Al...
In step 2 for Alice, what is the purpose of including Bob's public key in the hash? you can include a timestamp to prevent replay attacks instead. In step 2 for Bob, there is a typo - should use Alice's public key instead of her private key. Actually your protocol is similar to PGP, and I dont think it provides d...
I have the following problem: Alice wants to send Bob a message such that Bob knows it is from Alice but at the same time he cannot prove that Alice send him this message. The solution I came up with, using RSA, is: 1. Alice picks a random key K, and encrypts the message M using this key K. M'= aes(K, M) 2. Al...
The [specification][1] doesn't seem to indicate how to pad messages to the requisite 512-bit boundary. What is the padding scheme for the original Tiger hash? [1]: http://www.cs.technion.ac.il/~biham/Reports/Tiger/tiger/node3.html#SECTION00030000000000000000
This is a spectacularly ambiguous, poorly-posed question, so I'm going to instantiate it in a way that I find interesting. If this wasn't the question you wanted answered, then edit your question to do a better job of asking a well-formed question. ---- $\newcommand{\tri}{\mathbin{\triangle}}$ I'm going to assu...
I am trying to implement [Efficient Robust Private Set Intersection](http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf) using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs. q = 17 (prime), g = 6 (generator), x = 5 (private key), public key = g^x mod p = 6...
**Edited to clarify question** So my question is whether anyone knows of an efficient way to compute the neutral element (I'm gonna call it 1, but the operation doesn't have to be multiplication) in an abstract ring isomorphic to $\mathbb Z/ N\mathbb Z$? More specifically, the scenario is this: Suppose we have a ...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
I have read that in cases where there is a limit on the amount of data sent over the network, one idea is to sent only t bits of data rather than sending all the bits. For example in Schnorr scheme this can be employed. Whether this can be specified by sending the t bits along with the other information?
I'm not cryptography expert (well, i'm here after all!) but i have this dubt: Suppose i have 2 different keys: 1. secretkey1 2. secretkey2 And a plain text: - myReallySecretPlainText if i use **AES128** on my plain text with my first key i get this: U2FsdGVkX19fHxumDqEB9Kuyvhj+aoHpctLCdo2VEvt1...
Does re-iterate AES128 with different keys gives any benefict?
I am trying to implement [Efficient Robust Private Set Intersection](http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf) using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: - $p = 17$ (prime) - $g = 6$ (generator) - $x = 5$ (private key) - $k = ...
Why are Fermat primes (2^2^n+1) useful as e (the public key) in RSA encryption? I understand why 2^n+1 primes are useful, because they would simply be 100...001 in binary, which for computers is faster in calculations. But why is it important that the exponent is also a power of 2?
I'm not cryptography expert (well, i'm here after all!) but i have this dubt: Suppose i have 2 different keys: 1. secretkey1 2. secretkey2 And a plain text: - myReallySecretPlainText if i use **AES128** on my plain text with my first key i get this: U2FsdGVkX19fHxumDqEB9Kuyvhj+aoHpctLCdo2VEvt1...
Why are Fermat primes ($2^{2^n+1}$) useful as $e$ (the public key) in RSA encryption? I understand why $2^n+1$ primes are useful, because they would simply be `100...001` in binary, which for computers is faster in calculations. But why is it important that the exponent is also a power of 2?
Why are Fermat primes ($2^{2^n}+1$) useful as $e$ (the public key) in RSA encryption? I understand why $2^n+1$ primes are useful, because they would simply be `100...001` in binary, which for computers is faster in calculations. But why is it important that the exponent is also a power of 2?
I am currently implementing Shamir's ID based signature algorithm as proposed in [Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984.][1] However I am stuck with generating the private key for a certain i...
I am currently implementing Shamir's ID based signature algorithm as proposed in [Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984.][1] However I am stuck with generating the private key for a certain i...
I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: p=17 (prime) g=6 (generator) x=5 (private key) k=gx(modp)=65(mod17)=7 (public key) Suppose the clients inputs are 1, 2. Then P(x)=(x...
I try to understand the PACE-Protocol, especially the Key Derivation Function in ECDH. https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/TechGuidelines/TR03110/TR-03110_v2.1_P3pdf.pdf;jsessionid=9EC0D52B40D9E3BA7C46108E9E1C4530.2_cid374?__blob=publicationFile Page 33: Can someone explain me, wha...
I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: p=17 (prime) g=6 (generator) x=5 (private key) k=gx(modp)=65(mod17)=7 (public key) Suppose the clients inputs are ...
While maintaining a constant rate of data transfer is one way to thwart traffic analysis, I think there are other ways, too. Maybe this is only a half-baked idea, but wouldn't it be sufficient to maintain any fixed distribution of data transfer? E.g., use a fixed packet size, and send packets at times that are indis...
I try to understand the [PACE-Protocol](https://www.bsi.bund.de/SharedDocs/Downloads/EN/BSI/Publications/TechGuidelines/TR03110/TR-03110_v2.1_P3pdf.pdf), especially the Key Derivation Function in ECDH on page 33. Can someone explain me, what the Counter is good for? Often there are iteration counters in KDF - but he...
Can you explain the counter in the Key derivation function of PACE?
When doing password-based encryption, is it OK to create one instance of **PBKDF2** from the password, and then use it to create both the **AES** key and the **MAC** key? (Or should a new instance of PBKDF2 be created using a different salt or iteration count, for each?) [This answer][1] seems to say this isn't a...
Derive both MAC and AES keys from same PBKDF2?
is [this attack][1] practical to break [original recommended implemented widely used] *Binary Goppa code* in $2^{44}$ computation? if the answer is yes then how much for $n , k , t$ you suggest to be safe? or we need to use another code /curve ? [1]: http://arxiv.org/abs/1401.6025
I have read that in cases where there is a limit on the amount of data sent over the network, one idea is to sent only $t$ bits of data rather than sending all the bits. For example, in the Schnorr scheme this can be employed. My question is, whether this can be specified by sending the $t$ bits along with the other...
How to specify last $t$ bits are only sent when a signature is sent?
I am reading the page 38 in this ["Post Quantum Cryptography" book][1] (Equations 8 and 9). My question is, why to compute the verification key $Y$, $f$ is applied $2^w-1$ times? Are there any security notions involved? [1]: http://www.e-reading-lib.org/bookreader.php/135832/Post_Quantum_Cryptography.pdf
In the section 3 (page 44) of the book ["Post Quantum Cryptography"][1], it says: > Then each one-time signature key must be generated twice, once for the MSS public key generation and once during the signing phase. Also defined $\text{PRNG}$: $\text{Seed}_{\text{in}} \rightarrow (RAND, SEED_{\text{out}})$, whe...
Merkle signature + PRNG?
In the section 2 (page 42) of the book ["Post Quantum Cryptography"][1], it says: > Then he generates the one-time signature $\sigma_{\text{OTS}}$ of the digest using the $s$-th one-time signature key $X_s$, $s\in\{0,\dots,2^H-1\}$. My question: Is $s$ chosen in random form? Is it possible to have $s$ collision...
I am studying LogSpace Merkle Tree Traversal algorithm in ["Post Quantum Cryptography"][1]. I don't understand the Table 1 on page 58. My question is: Why within of the $2^h$ rounds for $NEED_h$ exist only one $TAIL$, if tail in the page 42 is defined than intermediate nodes in $STACK_h$? ![image of"Treehash" de...
I am studying LogSpace Merkle Tree Traversal algorithm in ["Post Quantum Cryptography"][1]. I don't understand the Table 1 on page 58. My question is: Why within of the $2^h$ rounds for $NEED_h$ exist only one $TAIL$, if tail in the page 42 is defined than intermediate nodes in $STACK_h$? > **Algorithm 2.1** Tre...
What does the following notation mean in a homomorphic encryption scheme? ENC(x;r). What does 'x' and 'r' refer to?
With Pubic Key (G, q, g, h) ENC (X;r) = (g^r, h^r . g^m) mod q. Is my interpretation right?
Is the logarithm in the private set intersection protocol mentioned in Section 3.4, Step 5 of http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf, a base 10 or 2? How do we find this out?
I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 of [this paper](http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf) on the following inputs: p=17 (prime) g=6 (generator) x=5 (private key) ...
I've been reading up a bit on deterministic password generators. All the ones I can find basically do something like this: 1. Pick a master username and a master passphrase. The username could be your email, or a PIN, or something else. The master passphrase can be subject to stringent requirements to ensure suffici...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
I've seen that there is several kinds of PRF, and sometimes people speak about strong PRFs. When proofs of a protocol or algorithm are given based on the assumption of the use of a PRF, are they speak implicitly about strong PRFs?
I read many papers on authenticated key exchange protocols, and most security proofs are done by the authors. In this method, you can imagine that the efficiency is low. Moreover, even if you have proven an AKE protocol's security under a certain model (say [eCK][1]), you still cannot ensure the security under all othe...
There's a new e-print out on arXiv titled ["A Polynomial Time Attack against Algebraic Geometry Code Based Public Key Cryptosystems"](http://arxiv.org/abs/1401.6025) by Alain Couvreur, Irene Márquez-Corbella and Ruud Pellikaan: > "We give a polynomial time attack on the McEliece public key cryptosystem based on alge...
Is the Couvreur et al. polynomial time attack on McEliece practical?
I am currently implementing Shamir's ID based signature algorithm as proposed in [Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984.][1] However I am stuck with generating the private key for a certain i...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
I am trying to implement [Efficient Robust Private Set Intersection](http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf) using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: - $p = 17$ (prime) - $g = 6$ (generator) - $x = 5$ (private key) - $k = ...
Suppose you want to select a prime $p$ such that finding e.g. $log_2(3)$ in $\mathbb{Z}_p$ is expected to be either at least as hard as the general Discrete Logarithm Problem in $\mathbb{Z}_p$, or at least both problems infeasible. How large would $p$ have to be? Intuitively, the problem of finding $log_2(3)$ seems ...
I am currently implementing Shamir's ID based signature algorithm as proposed in [Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984.][1] However I am stuck with generating the private key for a certain i...
I am trying to implement Efficient Robust Private Set Intersection using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: p=17 (prime) g=6 (generator) x=5 (private key) k=gx(modp)=65(mod17)=7 (public key) Suppose the clients inputs are 1, 2. Then P(x)=(x...
I am trying to implement [Efficient Robust Private Set Intersection](http://www.ece.umd.edu/~danadach/MyPapers/set-int.pdf) using additive ElGamal. I am trying to run the full protocol mentioned in Section 3.4 on the following inputs: - $p = 17$ (prime) - $g = 6$ (generator) - $x = 5$ (private key) - $k = ...
Suppose I have an encryption function $e$ of a symmetric cipher with plaintext space $M=\{1,2,\ldots,2^{24} \}$. Suppose we have a list $L$ of integers: $67; 114; 121; 112; 116; 111.$ Decoding with the ASCII encoding scheme gives the word Crypto. Now, my teacher says that there is a weakness in using the ASCII e...
As per request, some hints. Suppose you are an eavesdropper and you intercept the encryption of 'Crypto'. - What is the encryption of `p`? - What is the encryption of `CopytopCrypto`? - Suppose you intercepted a later message, which was either `Ya` or `No` (yes/no would be even easier to differentiate between s...
As per request, some hints. Suppose you are an eavesdropper and you intercept the encryption of 'Crypto'. - What is the encryption of `p`? - What is the encryption of `CopytopCrypto`? - If we were able to get the message `abc...zAB...Z .,"` encrypted, what messages could we calculate the encryptions of then? ...
Why do we need [HKDF-Expand][1] if we can simply hash the pseudorandom key to make it longer? The docs (in the link) say: > The second stage "expands" the pseudorandom key to the desired > length... Is it only to allow for longer keys? So that if all we need is, say, 32 bits - we can simply use SHA256? Or is th...
How is HKDF-Expand better than a simple hash?
I am currently implementing Shamir's ID based signature algorithm as proposed in [Adi Shamir, Identity-Based Cryptosystems and Signature Schemes. Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, 7:47--53, 1984.][1] However I am stuck with generating the private key for a certain i...
Suppose I have an encryption function $e$ of a symmetric cipher with plaintext space $$\mathcal{M}=\{1,2,\ldots,2^{24} \}.$$ Now, consider a list $L$ of integers: $$67, 114, 121, 112, 116, 111.$$ Decoding $L$ with the ASCII encoding scheme (see http://www.asciitable.com/) gives the word (plaintext) **Cr...
Suppose I have an encryption function $e$ of a symmetric cipher with plaintext space $$\mathcal{M}=\{1,2,\ldots,2^{24} \}.$$ Now, consider a list $L$ of integers: $$67, 114, 121, 112, 116, 111.$$ Decoding $L$ with the ASCII encoding scheme (see http://www.asciitable.com/) gives the word (plaintext) **Cr...
I am making a tool for myself where I intend to store cipher text. I wish to use AES together with arbitrary sized keys to create these cipher text strings. The idea is to use a cryptographic hash like sha256 to compensate for the key length issue. Is this a sound way of doing things? Also since the output domain o...
>Is this a sound way of doing things? Depends. Where do the keys come from? If they come from a user's memory (e.g., a password) then no. The reason for this is that a simple hash if fairly fast to compute. Typically we recommend people use something like PBKDF2 or [scrypt][1] as they run through thousands of iterat...
I've implemented a Rabin-Miller primality test fuction following Wikipedia and the book Applied Cryptography. Now I'm using it for generating primes with a string seed. The book suggests the following for this: 1. Generate a random 'n'-bit number 2. Set the high- and low-order bits to 1. 3. Make sure it i...
When encrypting with RSA it is often infeasible to decrypt by just doing `c^d mod n`, because eg. when using the primes (p,q)=(12553,1233), which are small primes compared to those in used by banks etc. One would often choose the Fermat number 65537 as public exponent e, then the private exponent d is 4267793, which is...
When encrypting with RSA it is often infeasible to decrypt by just doing `c^d mod n`, because eg. when using the primes (p,q)=(12553,1233), which are small primes compared to those in used by banks etc. One would often choose the Fermat number 65537 as public exponent e, then the private exponent d is 4267793, which is...
I am making a tool for myself where I intend to store cipher text. I wish to use AES together with arbitrary sized keys to create these cipher text strings. The idea is to use a cryptographic hash like SHA256 to compensate for the key length issue. Is this a sound way of doing things? Also, since the output domai...
When encrypting with RSA it is often infeasible to decrypt by just doing `c^d mod n`, because eg. when using the primes $(p,q)=(12553,1233)$, which are small primes compared to those in used by banks etc. One would often choose the Fermat number $65537$ as public exponent $e$, then the private exponent $d$ is $4267793$...
How do institutions like banks do RSA with big primes?
Using homomorphic encryption, I would like to be able to take an encrypted integer and either add 1 or -1 for a new encrypted value. I do not want the encrypted value to be recoverable - just the following: * $\varepsilon(x) = (\varepsilon(x) \oplus \varepsilon(-1)) \oplus \varepsilon(1) = (\varepsilon(x) \oplu...
Imagine there is a $n$ bit block cipher. The attacker has harvested some how all possible $2^n$ cipher texts for some given key. Without the knowledge of the distribution of input domain as in frequency counts or some statistical information of input data. Is it possible to perform ciphertext only attacks ? Any example...
is knowing the distribution of input domain only way to do cipher text only attacks?
When creating digital signatures is it ok to send part of it when we have bandwidth constraints?
Is it ok to send part of digital signature if we have bandwidth constraints?