instruction stringlengths 15 30k |
|---|
I'm sorry if my English is bad.
Let $N=PQ$, where $P=2p+1$ and $Q=2q+1$. $P,Q,p,q$ are prime numbers. $QR_{N}$ is the set of quadratic residues modulo $N$.
1. Please help me to prove $QR_{N}$ is a cyclic group. Note: $QR_{P}$ and $QR_{Q}$ are cyclic groups.
2. How to find/determine generator for $QR_{N}$?
|
I am trying to find an implementation or variant of a *(k, n)* threshold cryptosystem (as described here [Shamir's Secret Sharing][1]) where we can fix at least one of the *k* key parts, i.e., instead of ANY *k* key parts able to decrypt the ciphertext I want at least one of the *k* key parts to be a certain/fixed key ... |
I'm going to use the notation from [here](http://en.wikipedia.org/wiki/Goldwasser-Micali_cryptosystem).
I'm still not sure why one wants to handle $-1$ as a message, but anyways. Simple solution is that you simply define: if message is $-1$ set message to $1$ and the other way round when decrypting. Second point is ... |
I have a question regarding the paper "Fully Homomorphic Encryption over the Integers"
(http://eprint.iacr.org/2009/616.pdf): On page 6 after they set their parameters, it says
"This setting results in a scheme with complexity $\overset{\sim}{\mathcal{O}}(λ^{10}).$"
What exactly do they mean by this? That the ... |
I'm not talking about [scytale][1], but encryption like RSA, DES, etc...
In my question:
Public cryptography == Civil cryptography.
How did exactly civil cryptography evaluate after WWII?
[1]: https://en.wikipedia.org/wiki/Scytale |
Is it true, that public cryptography did appear in 50x-60x only thanks to leak from NSA? |
I suggested mulitiplicative secret sharing in an [answer to another question][1], but noted that I wasn't sure if it was even secure and was hoping someone would comment on the security. Since no one did, I thought I'd ask it as a separate question.
Fix a multiplicative group, say $\mathbb{Z}_p^*$.
To share $s$ w... |
Is multiplicative secret sharing secure? |
I'm not sure why in the Goldwasser-Micali encryption scheme with a Blum integer $N$, the message $-1$ is always a illegal message.
Can you give me some direction for starting?
What is illegal message's meaning? |
I'm not talking about [scytale][1], but encryption like RSA, DES, etc...
How did exactly civil cryptography evolve after WWII?
[1]: https://en.wikipedia.org/wiki/Scytale |
Is it true, that non-military cryptography appeared in 50's and 60's only thanks to leaks from the NSA? |
Currently I'm doing some initial research for a fully connected distributed network communication model. The context here is a peer-to-peer multiplayer protocol, using a majority-voting system. More specifically, it's distributed lockstep used in most (all?) RTS games; *somewhat similar* to: [Age of Empires][1].
Gi... |
I found this question about CBC-MAC forging and want to make sure I understand it:
Let a and be be two strings of block length one. Suppose the sender sends (a, CBC-MAC(a)), (b, CBC-MAC(b)), (a||b, CBC-MAC(a||b)). Find new messages / MAC pair which the attack can now forge from the messages / MACs given above.
Si... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
One of the earliest d... |
Would like to prompt users for a single passphrase to establish trust with separate normally but not always complimentary systems from one password input.
Essentially looking for a box where one password enters and two leaves where maximum of entropy is maintained and chance of using either output password to derive... |
I would like to prompt users for a single passphrase to establish trust with separate normally but not always complimentary systems from one password input.
I'm essentially looking for a box where one password enters and two leaves where maximum of entropy is maintained and the chance of using either output password... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's**
... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's**
... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's…**
... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's…**
... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's…**
... |
Let $ PRG: \{ 0, 1\}^n \rightarrow \{ 0, 1\}^{n+s}$ be a pseudo random generator and let $A$ be an inverter that runs in polynomial time, specifically:
$\large \mathbb P_{d \leftarrow PRG(U_n)}[ A(d) = v, PRG(v) = d] \ \ge \ \delta$
Show how to construct a polynomial distinguisher $B$ that uses $A$ to distinguish... |
The biclique attacks that break AES ([Biclique Cryptanalysis of the full AES][1]) appear to require decryption oracles to work, presumably because the key schedule of AES is weaker in the decryption direction, enabling better bicliques to be constructed starting from the ciphertext end. Which is to say, these attacks ... |
Can someone please explain how the ECDSA algorithm works to compute signature?
Is the message to be signed first "encrypted" using ECDSA and then the Hash of it is computed? Is this then verified before decryption?
How is the "authentication" purpose served here? Please explain.
Thank you. |
Can someone please explain what key sizes are required for the ECDSA algorithm?
I tried a 128 bit EC Key for SHA1withECDSA and it throws an error. However with 256 bit key I could run the algorithm. Therefore want to know what key sizes are required for the different ECDSA algorithm with SHA1 and SHA2.
Also, how d... |
I know nothing of encrypting. I'm not even sure how to tag this.
I wrote a program that can calculate this pretty quickly on my macbook pro 2.3GHz IntelCore i7. The two exponents are Mersenne primes, and no I did not use floats.
It calculated: ((2^756839)-1) * ((2^1257787)-1) = a number 606,463 digits long. The ex... |
Would this program be useful in cryptography? |
I can several possible questions in the original post, hopefully I'll manage to answer at least one of them here.
------------
**I have calculated a large $N$, with $\log_{10}(N)>600,000$. Is this suitable for RSA?**
[coming soon]
**Is my multiplication algorithm good for taking the product of Mersenne Prim... |
I can several possible questions in the original post, hopefully I'll manage to answer at least one of them here.
------------
**I have calculated a large $N$, with $\log_{10}(N)>600,000$. Is this suitable for RSA?**
We have that $\log_{10}(N)>6*10^5>2^{19}$, meaning $\log_2(N)>2^{19}$. Currently, implementation... |
I won't answer your question up to every detail, as I would have to write a book to answer the pretty broad question to full length. But I'll give you some hints as it would be wrong to let you think that non-military cryptography has appeared in 50's and 60's only thanks to leaks from the NSA!
**Before the 30's…**
... |
I can several possible questions in the original post, hopefully I'll manage to answer at least one of them here.
------------
**I have calculated a large $N$, with $\log_{10}(N)>600,000$. Is this suitable for RSA?**
We have that $\log_{10}(N)>6*10^5>2^{19}$, meaning $\log_2(N)>2^{19}$. Currently, implementation... |
I know nothing of encrypting. I'm not even sure how to tag this.
I wrote a program that can calculate this pretty quickly on my macbook pro 2.3GHz IntelCore i7. The two exponents are Mersenne primes, and no I did not use floats.
It calculated `((2^756839)-1) * ((2^1257787)-1)` = a number 606,463 digits long. The e... |
I'm looking for different approaches of proofs for the CBC security. What are the best contents about this subject ?
Thank you very much. |
I'm looking for different approaches to proofs for the security of CBC mode encryption. What are the best sources of information about this subject?
|
I'm trying to find a **bijective** function y=F(x) which should it would be easy to compute in one direction but hard to compute on the other, and preferably x and y belong to the same simple space {0..2^n-1}.
The hard direction should be preferably as hard as computing hash preimages, but it could also be that ther... |
Is there any bijective one-way function not based on number-theoretic hardness assertions? |
I have question "How user's identity by Certification Authority " is verified.
While understanding, I am considering the following mathematics..
--> User generates his private key and with the help of private key , he generates his public key.
--> Now user want to register his public key. For this, he has to sen... |
I'd like to use [OpenPGP authentication over TLS](http://tools.ietf.org/html/rfc6091), but lack of implementations made me use a temporary solution: an OpenPGP/X.509 bridge certificate.
The approach is very similar to the approach used in Foaf:
https://svn.java.net/svn/sommer~svn/trunk/misc/FoafServer/pgpx509/src... |
OpenPGP/X.509 bridge: how to verify public key? |
I've found an nice explanation with example on [Udacity](http://forums.udacity.com/questions/8002881/rsa-numbers-not-relatively-prime-to-the-modulus) so I will copy the post a bit modified and formatted.
Taking an example of RSA with numbers small enough to reason with:
primes $p_1=11$, $p_2=13$ $N = p_1 \times... |
1. While reading **"Certificateless Public Key Cryptography"** by Author Sattam S. Al-Riyami and Kenneth G. Paterson, they have considered generation of private keys from **Key generation center(KGC)**.
Why should KGC generate private keys since if it gets compramized it will break security ?
Will it be possible that... |
Are there any differences in operation between existing Diffie-Hellman specifications, especially those within the [RSA PKCS#3](http://www.emc.com/emc-plus/rsa-labs/standards-initiatives/pkcs-3-diffie-hellman-key-agreement-standar.htm), ANSI X9.42 and [RFC 2631](http://tools.ietf.org/html/rfc2631) standards?
|
While reading "[Certificateless Public Key Cryptography](http://eprint.iacr.org/2003/126.pdf)" by Author Sattam S. Al-Riyami and Kenneth G. Paterson, they have considered generation of private keys from **Key generation center(KGC)**.
Why should a KGC generate private keys since if it gets compramized it will break se... |
While reading "[Certificateless Public Key Cryptography](http://eprint.iacr.org/2003/126.pdf)" by Author Sattam S. Al-Riyami and Kenneth G. Paterson, they have considered generation of private keys by a Key Generation Center (KGC). If the KGC gets compromised it will break security, so why should a KGC generate private... |
I wish to encrypt credit card numbers one by one using asymmetric encryption on the command line.
My current approach is this:
Encrypt:
/usr/bin/openssl rsautl -encrypt -inkey 'myKey.pub' -pubin | /usr/bin/openssl enc -base64
Decrypt:
openssl enc -base64 -d | openssl rsautl -decrypt -inkey myKey.... |
Is encrypting credit card numbers one by with with rsautl secure? |
I'm studying McEliece and Multivariate Public Key cryptographic systems. The main problem here is the huge key size.
Is there any restriction in using lossless compression algorithms to fix this problem? |
Is there any restriction in using lossless compression algorithms for huge key sizes? |
I wish to encrypt credit card numbers one by one using asymmetric encryption on the command line. My current approach is this…
Encrypt:
/usr/bin/openssl rsautl -encrypt -inkey 'myKey.pub' -pubin | /usr/bin/openssl enc -base64
Decrypt:
openssl enc -base64 -d | openssl rsautl -decrypt -inkey myKey.pem... |
You can look at the time taken by the 3 DES Challenges :
- DES Challenge 1 = 140 days
- DES Challenge 2 = 41 days
- DES Challenge 3 = **56 hours**
Source: http://cs-exhibitions.uni-klu.ac.at/index.php?id=263 |
Let $N=PQ$, where $P=2p+1$ and $Q=2q+1$. $P,Q,p,q$ are prime numbers. $QR_{N}$ is the set of quadratic residues modulo $N$.
1. Please help me to prove $QR_{N}$ is a cyclic group. Note: $QR_{P}$ and $QR_{Q}$ are cyclic groups.
2. How to find/determine generator for $QR_{N}$?
|
Without taking into account security, which hash function is the fastest one among the following:
MD5, SHA-1, SHA-2 (for various internal size), Keccak, and other… ? |
I have question "How user's identity by Certification Authority " is verified.
While understanding, I am considering the following mathematics..
- User generates his private key and with the help of private key , he generates his public key.
- Now user want to register his public key. For this, he has to send ... |
I am read the Lemma 2 (pp13) in the paper "Kazukuni Kobara and Hideki Imai: Semantically Secure McEliece Public-Key Cryptosystems –Conversions for McEliece PKC– (PKC 2001)".
Related to the question "Why… for any $Hash_z$ and any $Gen$?", the author of the paper replies;
> The reason why "for any $Hash_z$ and an... |
Is encrypting credit card numbers one by one with rsautl secure? |
Following on from [here][1], I am unconvinced that encrypting twice with RSA is a waste of time: doesn't it depend on what is placed in-between the two encryptions?. What would happen if a permutation was applied at this point? How strong will the encryption be then?
That is,
$$f(m^{e_1}\mod n_1)^{e_2} \mod n_2$$
... |
This question is an extension of http://crypto.stackexchange.com/questions/1534/families-of-public-private-keys-in-elliptic-curve-cryptography
As described above, bitcoin "type 2" deterministic wallets use a root private/public key pair, where subsequent keys take advantage of the fact that in elliptic curve cryptog... |
Quoting "[Verified Security of Redundancy-Free Encryption
from Rabin and RSA](https://eprint.iacr.org/2012/308.pdf)", Chapter 2 (on page 4):
> OAEP was proved IND-CCA-secure by Fujisaki et al. [28] under the assumption that the underlying trapdoor permutation is partial-domain one-way. This is in general a stronger... |
Why $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ for RSA crypto? |
Most of the papers on block cipher constructions , especially the ones which discuss constructing block ciphers of arbitrary lengths or small domains, the techniques are designed based on building a PRP from a PRF . The ones that are based on luby rackoff etc .
Why is it that the input message first to be processed ... |
Why is it important to generate PRP from PRF? |
Are there are any cryptographic protocols or algorithms that can prevent active MITM attacks or interference when initiating a new connection to a server or someone you have not exchange keys with before?
For example:
**Alice's computer** -> **ISP** -> **Internet** -> **ISP** -> **Bob's server**
It is known th... |
Are there any protocols that are truly secure from active and passive MITM attacks? |
I am trying to sign certificate (X509) using secret sharing. that is shareholders combine their signatures to produce the final signature. which will be in this case the signed certificate. however practically from my understanding only one entity can sign a certificate. therefore I want to know:
> which entities or... |
I've received a public key to encrypt my data for the other end to decrypt using their private key. Now, they want us to sign the data as well to ensure non-repudiation.
I thought that I should only sign using a private key (which isn't in my possession)... How do I sign my encrypted data...?
Kind regards, |
How do I sign data that's been encrypted using public key? (RSA) |
Format preserving encryption has three modes FE1( FFX) , FE2(VAES) , FE3(BPS) . All of them are based on Feistel Networks .Can somebody explain how they differ from each other ? |
What is the different between various modes in FPE? |
I am trying to sign certificate (X509) using secret sharing. That is shareholders combine their signatures to produce the final signature which will be in this case the signed certificate. However practically from my understanding only one entity can sign a certificate. Therefore I want to know:
1. which entities or... |
I've received a public key to encrypt my data for the other end to decrypt using their private key. Now, they want us to sign the data as well to ensure non-repudiation.
I thought that I should only sign using a private key (which isn't in my possession). How do I sign my encrypted data?
|
Are there are any cryptographic protocols or algorithms that can prevent active MITM attacks or interference when initiating a new connection to a server or someone you have not exchange keys with before?
For example:
Alice's computer ➜ ISP ➜ Internet ➜ ISP ➜ Bob's server
It is known that ISPs are compromi... |
Most of the papers on block cipher constructions, especially the ones which discuss constructing block ciphers of arbitrary lengths or small domains, the techniques are designed based on building a PRP from a PRF. The ones that are based on Luby-Rackoff etc.
Why is it that the input message first to be processed by ... |
Why is it important to generate a pseudorandom permutation from a pseudorandom function? |
Are the proofs based on a PRF assumption still valid when using a variable-length input PRF ?
The answer is maybe obvious but I have a doubt.
|
I'm a University student with a lecturer who has no care of passion for the unit.
The Unit is Reliable and Secure Systems, but the lecturer offers no extra help, no further information. He simply reads off another teachers notes and then leaves 15-20 minutes early whilst we copy up someone else's notes.
As such... |
What does this Authentication protocol achieve and what information is shared? |
I'm going to use the notation from [here](http://en.wikipedia.org/wiki/Goldwasser-Micali_cryptosystem).
I'm still not sure why one wants to handle $-1$ as a message, but anyways. Simple solution is that you simply define: if message is $-1$ set message to $1$ and the other way round when decrypting. Second point is ... |
I am trying to learn everything I need to know for a Unit on 'Reliable and Secure Systems', but am struggling with the basics now.
![Protocol][1]
[1]: https://i.stack.imgur.com/NjUNK.png
The question that goes with this is:
> What is the purpose of the protocol, and how does it achieve this purpo... |
I am trying to learn everything I need to know for a Unit on 'Reliable and Secure Systems', but I'm struggling with the basics now.
The question that I'm having trouble with is:
> "What is the purpose of the protocol, and how does it achieve this purpose and what shared information does A and B end up after run... |
I was just reading Ars Technica's [primer on ECC](http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/2/). Somewhere near the middle of the second page, the author introduces the "dot" operation that takes an elliptic curve and two other known points, giving a t... |
In elliptic curve cryptography, how is "A dot A" computed? |
In order to be indistinguishable with respect to multiple messages, wouldn't the scheme need to be nondeterministic? How would this then possibly be vulnerable to an adaptive CPA? |
How can an encryption scheme be indistinguishable with multiple messages but vulnerable to an adaptive chosen-plaintext attack? |
For RSA cryptography, we know that the modulo $n$ is a product of two big prime numbers(say $p$ and $q$). However, in some documents I see an extension of $p=2p'+1$ and $q=2q'+1$ with $q'$ and $p'$ being huge prime numbers.
Why is it necessary to have $n=pq$ with $p=2p'+1$ and $q=2q'+1$ instead of just $n=p'q'$ when... |
What is the best algorithm to encrypt files for storage on untrusted servers? |
I'm working on a little personal project where security is very important, and I've thought for a while about the best way to do this. Now I am looking for a little outside help on good practices. The goal is to store personal text data on a server (like wifi passwords, etc) and be obtained through a password. I wanted... |
I am a hobby programmer with a background in biology and have developed an encryption program based on DNA. I tried to make it hard to crack, but it's essentially a substitution cipher and uses the default Java random number generator so my guess it could be cracked relatively easily. But how do I find out how good my ... |
How do I test my encryption? (absolute amateur) |
Why is an IV used in Merkle-Damgard transform? |
DES uses 16 rounds of feistel networks but not considered secure . Where Luby Rackoff constructions which are inspired by DES its proven by Patarin that 7 rounds is secure .
Is there a relation between number of rounds in DES and patarin's results ? |
Is there a relation between security of rounds of DES and Luby Rackoff rounds? |
I've seen that there is several kind of PRFs, 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, they speak implicitely about strong PRFs ?
Thank you.
|
In easy steps, this is how it works:
1. Convert txt to numbers. mod 1-26.
2. Generate random numbers (by my other cipher) equal to plain txt.
3. Write random numbers under txt numbers.
Like this:
txt = LOI - txt number = 12 15 09 - random number = 73 96 14
Encryption system, random numbers under txt n... |
Can someone tell if my Hand Cipher is secure? |
I've seen that there is several kind of PRFs. 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, they speak implicitly about strong PRFs? |
I've read those 2 questions & answers:
http://crypto.stackexchange.com/questions/5180/messages-of-different-lengths-and-one-time-computationally-secret
http://crypto.stackexchange.com/questions/5146/why-is-a-non-fixed-length-encryption-scheme-worse-than-a-fixed-length-one
I still not convinced of what is the a... |
Would the property of perfect forward secrecy still be achieved in MTI/A0 for a session key that was established between C and D when one LL-key aD is revealed so that both LL-keys aC and aD are revealed? |
Is there any way to generate values only between 0 and 255 with Diffie-Hellman method?
I need to create keys to comunication algorithms with 32 and 16 numbers between that range.
The ideia is to exchange the keys between the internet with the results of the diffie-hellman method and then create the keys on the cl... |
Can Diffie-Hellman generate values between x and y? |
Is there any way to generate values only between 0 and 255 with Diffie-Hellman method? I need to create keys to communication algorithms with 32 and 16 numbers between that range.
The idea is to exchange the keys between the participants using the results of the Diffie-Hellman key agreement algorithm. Then we create... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.