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I am study hash functions. I get understand colision resistance imply second pre-image resistance, but I can't get, yet, Why Second pre-image imply pre-image resistance?. Anybody Could be help me with this proof please? ![enter image description here][1] [1]: https://i.stack.imgur.com/raveV.png
I am study hash functions. I get understand colision resistance imply second pre-image resistance, but I can't get, yet, Why Second pre-image imply pre-image resistance?. Anybody Could be help me with this proof please? > ![enter image description here][1] [1]: https://i.stack.imgur.com/raveV.png > This is d...
I would like to perform some benchmarking of different block and stream ciphers for general data (lossless and lossy data) encryption and decryption (with focus on power consumption). To get general idea, I guess it probably would be better to use existing tools then to implement everything myself, then I can implem...
How to perform benchmark of data ciphers?
Let me try to elaborate on their proof. Suppose you had a hash function $H$ that was second-preimage resistant but *not* first-preimage resistant. By showing that this leads to a contradiction, we will be showing that with second-preimage resistance, you must have first-preimage resistance. Namely, we will show that th...
How to perform benchmark of block/stream ciphers?
I would like to perform some benchmarking of different block and stream ciphers for general data (lossless and lossy data) encryption and decryption (with focus on power consumption). To get general idea, I guess it probably would be better to use existing tools than to implement everything myself, then I can implem...
I am studying for an exam right now. And I wanted to make sure I got this point correct. AES is not a fiestel cipher because the operations in AES are not invertible. Is the above statement correct. If not, why isn't it a fiestel cipher?
I am a first year math PhD student with work experience and an MS in math. Do you have any advice regarding internships involved with cryptography and other mathematics other than the NSA? Thanks.
How to attack a fixed LCG with partial output?
<br/> I'm trying to programming Cardan grille method, but I can't find requirements for grille. In my case grille is square matrix A with NxN size, and elements are 0 or 1 (1 means that it is hole). I realized that if N is odd, central element of matrix can not be 1.<br/> What else?<br/> Thanks.
I am studying for an exam right now. And I wanted to make sure I got this point correct. AES is not a Feistel cipher because the operations in AES are not invertible. Is the above statement correct? If not, why isn't it a Feistel cipher?
Why is AES not a Feistel cipher?
The BLS digital signature says as follows: **Key Generation :** Pick random $x\xleftarrow{R} \mathbb{Z}_p^*$, and compute $v\gets g^*$, the public key is $v$, the secret key is $x$. **Signing :** Given a secret key $x$, and a message $M\in\{0,1\}^*$, Comupte $h\gets h(M)$ and $\sigma\gets h^x$ The signature i...
are there some attacks against BLS digital signature?
I read ampersand's question ["Necessity for finite field arithmetic and the prime number p in Shamir's Secret Sharing Scheme"](http://crypto.stackexchange.com/questions/5502/necessity-for-finite-field-arithmetic-and-the-prime-number-p-in-shamirs-secret), where he asked why Shamir's Secret Sharing Scheme uses arithmetic...
Why does Shamir's Secret Sharing Scheme need a finite field?
The answer to [this question][1] is clear about what a trapdoor function is, but what makes a trapdoor function $injective$ ? [1]: http://crypto.stackexchange.com/questions/10087/meaning-of-trapdoor-in-cryptography
what is an injective trapdoor function?
Short answer to the question is 'no', if the users of the service can choose their passwords. **Details** *If PIN or password is used?* There is no way to force people to select passwords that are secure. When password is long, at least some (lazy) users will make passwords that are long, but contain little en...
I'm trying to programming Cardan grille method, but I can't find requirements for grille. In my case grille is square matrix A with NxN size, and elements are 0 or 1 (1 means that it is hole). I realized that if N is odd, central element of matrix can not be 1. What else?
Cardan grille... what are requirements for grille?
Assume that sender and recipient both already have each others public keys(certificates). Sender needs to generate session key to encrypt some data and sends encrypted data to recipient. All offline - without interaction steps. But Sender must be authenticated. Could you advise well-known key management protocol to sol...
I was reading about the TIK protocol for thwarting wormhole attacks on adhoc networks. It uses a Merkel Hash Tree to store keys. But since the number of keys can be large, the tree is optimized by only storing the upper levels. As far as I understand, the a node is the result of the hash of its two children. But wh...
How are the lower levels calculated using upper levels in an optimized Merkel Hash Tree?
The BLS digital signature says as follows: **Key Generation :** Pick random $x\xleftarrow{R} \mathbb{Z}_p^*$, and compute $v\gets g^x$, the public key is $v$, the secret key is $x$. **Signing :** Given a secret key $x$, and a message $M\in\{0,1\}^*$, Comupte $h\gets h(M)$ and $\sigma\gets h^x$ The signature i...
The answer to [this question at Crypto.SE][1] is clear about what a trapdoor function is, but what makes a trapdoor function *"injective"*? [1]: http://crypto.stackexchange.com/questions/10087/meaning-of-trapdoor-in-cryptography
I'm trying to programm the Cardan grille method, but I can't find requirements for grille. In my case, grille is square matrix A with $N$ x $N$ size, and elements are $0$ or $1$ (where $1$ means that it is hole). I realized that if $N$ is odd, central element of matrix can not be $1$. But what are the other requ...
The BLS digital signature says as follows: - **Key Generation :** Pick random $x\xleftarrow{R} \mathbb{Z}_p^*$, and compute $v\gets g^x$, the public key is $v$, the secret key is $x$. - **Signing :** Given a secret key $x$, and a message $M\in\{0,1\}^*$, Comupte $h\gets h(M)$ and $\sigma\gets h^x$ The s...
Are there known attacks against the BLS digital signature?
I was reading about the [TIK protocol for thwarting wormhole attacks on adhoc networks][1]. It uses a Merkel Hash Tree to store keys. But since the number of keys can be large, the tree is optimized by only storing the upper levels. As far as I understand, the $a$ node is the result of the hash of its two children....
In [this table of the "Crypto++ 5.6.0 Benchmarks"][1], for example, cryptographic algorithm performance is measured in cycles per byte for symmetric ciphers, and in cycles per operation for asymmetric ciphers. What does "cycle" here mean, exactly? And does one AES or RSA decryption always need the same amount of cy...
Short answer to the question is 'no', if the users of the service can choose their passwords. **Details** *If PIN or password is used?* There is no way to force people to select passwords that are secure. When password is long, at least some (lazy) users will make passwords that are long, but contain little en...
I'm trying to write a Vigenere decipher script. I defined a couple of possible keylengths using the Kasiski method, using roughly this method: - find recurring strings in the ciphertext between 3 and 12 characters - make a list of the distances between them - loop through the list of distances and calculate the gr...
I'm trying to write a Vigenere decipher script. I defined a couple of possible keylengths using the Kasiski method, using roughly this method: - find recurring strings in the ciphertext between 3 and 12 characters - make a list of the distances between them - loop through the list of distances and calculate the gr...
According to http://www.pgp.net/pgpnet/pgp-faq/pgp-faq-keys.html#key-public-key-forgery, key ID is some lower bits sequence from the modulus (i.e.. the `n` variable): "A PGP key ID is just the bottom 64 bits of the public modulus (but only the bottom 32 bits are displayed with pgp -kv)." I've a key pair. Accordin...
I want to ask you one question about digital signatures in PDF. We know that **if** our document have digital siganture, we can detect, if original document is **altered or not**. And if we want to prove owner identity, we use digital signatures. **QUESTION:** It's very simple to remove certificate from ...
An attack against the signature scheme over some group where DDH is easy, can be turned into a solver for the CDH problem over the same group, as is shown in Section 2.3 in the Asiacrypt paper you refer to. So what you are really asking is: In what groups where DDH is easy is CDH still hard? I would not use ellip...
I want to ask you one question about digital signatures as they are (for example) used when digitally signing PDFs. We know that *if* our document has a digital signature, we can detect if the original document has been altered or not. And if we want to prove owner identity, we use digital signatures. On the othe...
What security provide digitally signatures (like used when signing PDFs)?
According to http://www.pgp.net/pgpnet/pgp-faq/pgp-faq-keys.html#key-public-key-forgery, key ID is some lower bits sequence from the modulus (i.e. the $n$ variable): > A PGP key ID is just the bottom 64 bits of the public modulus (but only the bottom 32 bits are displayed with pgp -kv). I have a key pair. Accordi...
How can I determine the GPG/PGP key ID from the RSA modulus?
The winner of the AES competition has a structure that does not qualify as a Feistel cipher, as explained in answers to this [recent question][1]. However, most of the AES candidates, and all other finalists ([Serpent][2], [Twofish][3], [RC6][4], [MARS][5]) are Feistel ciphers, if we define that as a cipher transfor...
Why was the winner of the AES competition not a Feistel cipher?
I am just reading the DAA paper (http://eprint.iacr.org/2004/205.pdf, Appendix A). A party $\mathcal{I}$ generates two group elements $g' \in \mathrm{QR}_n$ and $h = g'^r \bmod n$ with $r \in_R \left| \mathrm{QR}_n \right|$. Now $\mathcal{I}$ wants to proof in zero-knowledge that $h$ has been created correctly, i.e. th...
What security do digital signatures provide (like used when signing PDFs)?
The winner of the AES competition has a structure that does not qualify as a Feistel cipher, as explained in answers to this [recent question][1]. However, most of the AES candidates, and <strike>all</strike> 3 our of 4 other finalists ([Twofish][2], [RC6][3], [MARS][4]) are Feistel ciphers, if we define that as a c...
The winner of the AES competition has a structure that does not qualify as a Feistel cipher, as explained in answers to this [recent question][1]. However, <strike>most</strike> many of the AES candidates, and <strike>all</strike> <strike>3 out of 4</strike> some other finalists ([Twofish][2], [MARS][4]) are Feistel...
As far as I understand it, the hardware key-fob two-factor systems such as RSA SecurID depend on secret algorithms, and employ tamper-resistant hardware to prevent reverse engineering. Is there some mathematical fact that prevents a system like SecurID from operating with open-source software (including the server a...
Is it possible to create an open-source SecurID?
The winner of the AES competition has a structure that does not qualify as a Feistel cipher, as explained in answers to this [recent question][1]. However, <strike>most</strike> many of the AES candidates, and <strike>all</strike> <strike>3 out of 4</strike> some other finalists ([Twofish][2], [MARS][4]) are Feistel...
Consider the situation of a nation state (Blue) at war with another nation state (Red). Blue wants to deploy a secure cipher that blue currently can not break, but they are considered that Red could reverse engineer the cipher and use it to secure Red's communication (Red is unable to develop it's own secure cipher). ...
Consider the situation of a nation state (Blue) at war with another nation state (Red). Blue wants to deploy a secure cipher that blue currently can not break, but they are considered that Red could reverse engineer the cipher and use it to secure Red's communication (Red is unable to develop it's own secure cipher). ...
The reason that a _field_ must be used in Shamir's reconstruction scheme is that the calculations used in the reconstruction need to divide one "number" by another, and division is not defined in $\mathbb Z$, the set of integers: $\frac{m}{n}$ is not necessarily a member of $\mathbb Z$. So, why not use $\mathbb R$,...
As far as I understand it, the hardware key-fob two-factor systems such as RSA SecurID depend on secret algorithms, and employ tamper-resistant hardware to prevent reverse engineering. Is there some mathematical fact that prevents a system like SecurID from operating with open-source software (including the server a...
I'm trying to programm the Cardan grille method, but I can't find requirements for grille. In my case, grille is square matrix A with $N$ x $N$ size, and elements are $0$ or $1$ (where $1$ means that it is hole). I realized that if $N$ is odd, central element of matrix can not be $1$. But what are the other requ...
NIST is working on standardizing SHA-3. They have selected Keccak as the basis for SHA-3, and they plan to make some small changes to it; the result (with NIST's changes) will be standardized as SHA-3. A [blog post from the CDT](https://www.cdt.org/blogs/joseph-lorenzo-hall/2409-nist-sha-3) raises concerns over tho...
Are NIST's changes to Keccak/SHA-3 problematic?
NIST is working on standardizing SHA-3. They have selected Keccak as the basis for SHA-3, and they plan to make some small changes to it; the result (with NIST's changes) will be standardized as SHA-3. A [blog post from the CDT](https://www.cdt.org/blogs/joseph-lorenzo-hall/2409-nist-sha-3) raises concerns over tho...
There does appear to be some confusion with point 1. [This slide](http://csrc.nist.gov/groups/ST/hash/sha-3/documents/kelsey_ches2013_presentation.pdf#page=45) from Kelsey's presentation at CHES2013 says that there will be 4 different output versions (224, 256, 384 and 512) as well as 2 variable length output versio...
I am just reading the DAA paper (http://eprint.iacr.org/2004/205.pdf, Appendix A). A party $\mathcal{I}$ generates two group elements $g' \in \mathrm{QR}_n$ and $h = g'^r \bmod n$ with $r \in_R \left| \mathrm{QR}_n \right|$. Now $\mathcal{I}$ wants to prove in zero-knowledge that $h$ has been created correctly, i.e. th...
There does appear to be some confusion with point 1. [This slide](http://csrc.nist.gov/groups/ST/hash/sha-3/documents/kelsey_ches2013_presentation.pdf#page=45) from Kelsey's presentation at CHES2013 says that there will be 4 different output versions (224, 256, 384 and 512) as well as 2 variable length output versio...
I don't know where you get that the central element can not be $1$, because the Cardan grille does not have any special *"requirements"* as you're implying. In the original version, a piece of cardboard has several holes cut in it (= the grille) and when it is placed over an innocent looking message, the holes cover al...
Reading the [CHES'13 presentation by John Kelsey](https://docs.google.com/file/d/0BzRYQSHuuMYOQXdHWkRiZXlURVE/) does make things clearer. Basically, the whole thing (with the output lengths and capacities) seems to come down to the fact that NIST wants to standardize two versions of the underlying sponge function, S...
I don't know where you get that the central element can not be $1$, because the Cardan grille does not have any special *"requirements"* as you're implying. In the original version, a piece of cardboard has several holes cut in it (= the grille) and when it is placed over an innocent looking message, the holes cover al...
I'm trying to understand the framework of reactive simulatability using *"PfWa2_00AsyncModel"* from [this publication][1] which is a tech report behind the paper A model for Asynchronous Reactive Systems and its Applications to Secure Message Transmission by Pfitzmann and Waidner. I'm troubled with the remark 2.7 o...
I'm trying to program the Fleissner grille method, which is different from a Cardan grille, but I can't find requirements for grille. In my case, grille is square matrix A with $N$ x $N$ size, and elements are $0$ or $1$ (where $1$ means that it is hole). I realized that if $N$ is odd, central element of matrix can...
Fleissner grille... what are requirements for grille?
There does appear to be some confusion with point 1. The confusion probably stems from the fact that Keccak has an output size number and a capacity. Output size has little to no effect on security strength. Capacity is what really determines the security strength. So when the post says NIST will only standardize tw...
I don't know where you get that the central element can not be $1$, because the Cardan grille does not have any special *"requirements"* as you're implying. In the original version, a piece of cardboard has several holes cut in it (= the grille) and when it is placed over an innocent looking message, the holes cover al...
NIST is working on standardizing SHA-3. They have selected Keccak as the basis for SHA-3, and they plan to make some small changes to it; the result (with NIST's changes) will be standardized as SHA-3. A [blog post from the CDT](https://www.cdt.org/blogs/joseph-lorenzo-hall/2409-nist-sha-3) raises concerns over tho...
I don't know where you get that the central element can not be $1$, because the Cardan grille does not have any special *"requirements"* as you're implying. In the original version, a piece of cardboard has several holes cut in it (= the grille) and when it is placed over an innocent looking message, the holes cover al...
What are requirements for this grille?
Who's talking to who encryption - does this concept work?
I'm trying to program a <del>Cardan</del> grille, but I can't find requirements for grille. In my case, grille is square matrix A with $N$ x $N$ size, and elements are $0$ or $1$ (where $1$ means that it is hole). I realized that if $N$ is odd, central element of matrix can not be $1$. But what are the other req...
Actually, that wikipedia article you mention in your question already answers your question: > It is moderately common for companies and sometimes even standards bodies as in the case of the CSS encryption on DVDs – to keep the inner workings of a system secret. Some argue this "security by obscurity" makes the pro...
When using the curve25519 DH function, D.J. Bernstein recommends hashing the shared secret before using it as a session key for a symmetric block cipher. Why is that? Hashing won't increase the entropy. Do the shared secrets from a curve25519 have some non-random properties that could be exploited if the shared secr...
Why must curve25519 shared secret be hashed?
I'm having a hard time understanding the elleptic curve encryption. One thing thing I don't understand is listing all the points on the curve (mod p). Supose I have the following elliptic curve: y^2 = x^3 + 2x + 3 (mod 5). To find the list of all the points you run through 0 < x <= 4 and solve for y. I know the out...
I'm having a hard time understanding the elliptic curve encryption. One thing thing I don't understand is listing all the points on the curve (mod p). Suppose I have the following elliptic curve: y^2 = x^3 + 2x + 3 (mod 5). To find the list of all the points you run through 0 < x <= 4 and solve for y. I know the ou...
I'm not sure I get your Q? but do these links help - http://people.csail.mit.edu/rivest/crypto-security.html#Software (Eric Young's DES implementation) - http://www.tero.co.uk/des/ - http://www.opensource.apple.com/source/OpenSSL/OpenSSL-26/openssl/crypto/aes/ - http://www.opensource.apple.com/source/Ope...
From the [court decision][1], we find out that the researchers didn't in fact reverse engineer the key transponders themselves, but a piece of software called "Tango Programmer" which is a third party tool (software and hardware) used to make transponders. [Tango Programmer][2] is readily available, but it appears t...
I'm having a hard time understanding the elliptic curve encryption. One thing thing I don't understand is listing all the points on the curve (mod p). Suppose I have the following elliptic curve: y^2 = x^3 + 2x + 3 (mod 5). To find the list of all the points you run through 0 < x <= 4 and solve for y. I know the o...
Read a post on [Schneiers blog][1] ([and again 2011][2]) about increasing the number of rounds for AES from to "*AES-128 at 16 rounds, AES-192 at 20 rounds, and AES-256 at 28 rounds*" to raise the security. However, I did wonder where these figures came from. According to Schneier "*hey're off the top of my head, and c...
folks! I have this service, and I want to authenticate my clients using SSL client certificates. Now I want the key exchange procress to be as simple as possible, kind of like SSH: You generate a keypair and upload the public key to the server (which you already trust). Now I want do verify the certs I get from t...
What is the expert cryptographic opinion on the following? Assume that there is a web server and a client on web page. User on the Client calls an OTP web service on the server which: 1. creates a RSA key pair 2. generates a random 10 digit string - the Message 3. Encrypts the Message with the Public Key compon...
Suppose the attacker knows $X, Z$ such that $H(X || Y) = Z$ If `bit-length(Y) < 60` then a brute force attack is possible. What if `bit-length(Z) = 256` (such as in SHA-256), `bit-length(X) = 128`, or `bit-length(Y) = 256`? Are there any published paper with results/experiments with SHA-256/512 in full or red...
Two parties: a client and a server are to a agree on a symmetric key. Both the client and the server are aware of a `master password`. The way this is currently done is: 1. Both parties hash the `master password` using SHA-256 to create a `password hash`. 2. The `password hash` is used by the client to encrypt a ...
In a description of **IND-CPA** (indistinguishability under the chosen plaintext attack), I have been reading the following, simple test: > The adversary can generate as many plaintexts as he wants. Then, he chooses two messages $m0$ and $m1$, those messages are encrypted, and one of the ciphertexts is sent back to ...
Is this really the correct way to do an IND-CPA test?
In a description of **IND-CPA** (indistinguishability under the chosen plaintext attack), I have been reading the following, simple test: > The adversary can generate as many messages as he wants. Then, he chooses two messages $m0$ and $m1$, those messages are encrypted, and one of the ciphertexts is sent back to hi...
In a description of **IND-CPA** (indistinguishability under the chosen plaintext attack), I have been reading the following, simple test: > The adversary can generate as many messages as he wants. Then, he chooses two messages $m0$ and $m1$, those messages are encrypted, and one of the ciphertexts is sent back to hi...
I have a service and I want to authenticate my clients using SSL client certificates. Now I want the key exchange process to be as simple as possible, kind of like SSH: You generate a keypair and upload the public key to the server (which you already trust). Now I want to verify the certs I get from the clients… not...
I stumbled onto the explanation of Rijndael Rcon on Wikipedia, and I can't follow it. Can someone please explain. http://en.wikipedia.org/wiki/Rijndael_key_schedule The example for Rcon indicates that Rcon(9) is 0x1b. That could make sense...: rcon(9) = (2 ^ (9 - 1) mod (256)) + 16 + 8 + 2 + 1 But I don't under...
Rijndael: explanation of Rcon on Wikipedia?
I stumbled onto the explanation of [Rijndael Rcon on Wikipedia](http://en.wikipedia.org/wiki/Rijndael_key_schedule), and I can't follow it. The example for Rcon indicates that *Rcon(9)* is `0x1b`. That could make sense… `rcon(9) = (2 ^ (9 - 1) mod (256)) + 16 + 8 + 2 + 1` But I don't understand *Rcon(10)* or ...
I've done research about this subject, but I can't find the answer I'm looking for. The background: > I'm making a network service that is used to transfer small amounts of data (less than 100bytes 90% of the time), to a small amount of users. When a known users connects it will generate a new RSA key-pair and echo...
Hybrid encryption with RSA and AES versus spliting into multiple RSA messages?
I've done research about this subject, but I can't find the answer I'm looking for. The background: > I'm making a network service that is used to transfer small amounts of data (less than 100bytes 90% of the time), to a small amount of users. When a known users connects it will generate a new RSA key-pair and send...
There have been strict laws about the export of crypto software to certain countries. I can understand the intent, but never gauged the fact that there is nothing stopping these countries from developing their own crypto software. So why limit the export? And in light of the recent NSA revelations, of backdoors bei...