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When it comes to lattice based cryptographic systems, all the literature talks about, good bases and bad bases. How does one define what a good basis is and what a bad basis is?
I'm implementing the SRP-6 protocol, which relies on discrete logarithms for it's security (essentially Diffie-Hellman). The RFC documents state: The private values $a$ and $b$ SHOULD be at least 256-bit random numbers, to give approximately 128 bits of security against certain methods of calculating discrete logarith...
I think 1024 bit RSA keys were considered secure ~5 years ago, but I assume that's not true anymore. Can 2048 or 4096 keys still be relied upon, or have we gained too much computing power in the meanwhile? Edit: Lets assume an appropriate padding strategy. Also, I'm asking both about security of signatures and security...
Suppose the Hill cipher were modified to something like a one-time pad cipher, where Alice wants to send a message to Bob, and she chooses a key matrix randomly everytime a new message is sent (and the inverse of the key matrix is sent to Bob by other means everytime - just as in the one-time pad). Would this yield per...
Imagine a Field Isomorphism $g : \mathbb F1 \to \mathbb F2$ given by some $g(x)$ Assume a client is planning to outsource his computations to server, translates every possible $x$ as $g(x)$ and sends to server and once he gets the result he translates g inverse to get the answer. I know the above is straw man solution...
What is the computational cost of a certificate signature verification in terms of exponentiation, multiplication and other computation operations?
What is “Implicit Authentication” in the context of authentication methods? I searched the Web but could not find any article that describes this. If anyone can describe it, that would be a great help.
Possible Duplicate: Would the ability to efficiently find Discrete Logs have any impact on the security of RSA? I'm wondering if breaking the DLP, that is the basis for ElGamal and DSA, would automatically break RSA. The way I see it, RSA is based on the following three assumtpions, please correct me if I'm wrong. ...
Let me ask about my toy passwords generator program X5 which I want to improve. X5 uses a secret key and a public key to generate a password.Where any public key is supposed to be known to hackers in the worst case. pwd = sK + pk To describe details, let me define some expressions. each of K and k denotes a seed key ...
I was wondering if the prime numbers defined for use with Diffie-Hellman in RFC 3526 are more trustworthy than generating one's own, especially considering the recent Arjen Lenstra paper (Ron was wrong, Whit is right) which criticized the similarities detected in public keys and prime numbers across the Internet. Am I ...
I'm looking into implementing a private SILC server for friends (and possibly their friends). And after visiting the Wikipedia entry for SILC protocol, it seems all the official pages linked at the bottom are dead with only a few anon servers here and there. Is it still being used nowadays? And if it is ... where(onlin...
I am curious, is there any paper where SHA-3 competitors are compared in terms of energy efficiency?
For a project I wonder if there exists some kind of fixed-size checksumming/fingerprinting function in which based on this fingerprint given data block 1, it is easy to generate more data blocks that share the same fingerprint/hash key. Therefore this is unlike an MD5 sum. (In that I don't know how to easily go back fr...
I just read this article on Wikipedia: Certificate Signing Request I'm not a PKI or Crypto expert. As I understand, a CSR (certification request) is always signed by the PKCS#10-Request creator. What I don't understand is why the CA, which receives and processes the CSR, then removes this signature (I mean, without th...
I need to implement the HASH algorithm (MD5 & SHA-1) on an 8 bit MCU. I hear it can only be implemented on 32bit and sometimes 16bits MCU. Is that possible? I will appreciate link where possible. A program in C language most preferred.
This might be out of ignorance, I apologize, but how complex of a problem might it be to generate a file of size $N$ whose MD5SUM is $X$? For example, ls -l wczasp.rb -rwxrwxrwx 1 master master 7273877 2011-01-30 17:13 wczasp.rb md5sum wczasp.rb acf3602b5eb9a2db3e365d3043682faf wczasp.rb So, how computationall...
Suppose Alice would like to obtain the product of two mXm matrices i.e. A and B. Alice has A, whereas Bob has B. Since Alice does not want to reveal A to Bob, she chooses a mXm random invertable matrix R. She sends R*A to Bob over a secure channel. Bob obtains R*A, and calculates R*A*B, and sends it to Alice over a se...
I was wondering why the Fujisaki-Okamoto construction (or one of its variants) is not (at least commonly) used with RSA to achieve CCA2 security? Does anyone know of any speed comparisons between RSA w/ F-O and RSA-OAEP? Perhaps the reason is simply historical since F-O is newer.
I'm not sure I understand really the implications of proofs of security in the random oracle model. Does a proof of security in ROM translate to a reduction of security of the crypto-system to the security of the hash function in the standard model? If not, then this would imply that the meaning of the ROM proof in the...
I am a software developer working on an application with the .NET platform. This application needs to provide a secure connection and encrypt all data between the client and the server. It is a standaone app that does not use a web browser and will be using a symmetrical key for the vast majority of the messages for ...
Suppose I generate a random $m×m$ matrix $R$, where each of its elements belongs to $\mathbb Z_n$. I ensure that $R$ is invertible in $\mathbb Z_n^{m×m}$. Now I take a non-random $m×m$ matrix $A$, where each of its elements belongs to $\mathbb Z_n$ and is not zero. I now multiply them both together to obtain $R·A$ and ...
When I need to generate unique id's based on some information hashing is typical choice. However, sometimes that id needs to be of a particular size. I've seen a lot of schemes (HMAC-MD5-96 in SSH, CGA in SeND for IPv6) that use a portion of a hash, so I'm thinking it might be alright to use it that way. Which prope...
What's the difference between the "Signature Algorithm" and the "Signature Hash Algorithm" found in an X.509 certificate? Why does it need a "Signature Hash Algorithm"? Edit: I'm creating the X.509 cert with PHP 5.2. When I change the 'digest_alg' to 'md5', both properties of the Microsoft Cert Tool changes to md5. So...
I'm wondering why we use encrypt-decrypt-encrypt (EDE) sequence in 3DES (also known as DES-EDE, TDES or TDEA) with three keys instead of three times encryption (EEE) with three different keys?
This is mostly a terminology question, but I suppose that it is best asked and answered here. After browsing the Internet I have come across a fair number of completely different definitions of the term "key stretching" and would like to know if there is any consensus in the research literature about how the term is to...
I am wondering what the complexities are of adding/subtracting and muliplying/dividing numbers in a finite field $\mathbb{F}_q$. I need it to understand an article I am reading.
CFB, OFB and other modes are meant for streaming and don't require padding. Are there still limitations such as the text needs to be greater than key length?
When creating padding for RSA using OAEP, a message is prepared as follows: Hash(Input Parameter) || Zeros || 1 || Message My question is, what should the Input Parameter be? It must be known to both sides, I understand it can be an empty array (string, whatever). In that case there is no need to calculate the hash, h...
Assuming a bit string is deemed cryptographically secure, e.g. PRNG using AES in counter mode, can we equally assume any permutation of said bit string is also cryptographically secure? In a more practical sense, using a PRNG with AES in counter mode again (for instance), assume it turns out that AES can be more effici...
Is division possible in the Paillier Cryptosystem? i.e. given a the cipher-text $C$ of an integer $M$ the plain-text divisor $D$, and only the public key, can one compute the cipher-text of $M/D$ ?
Why is CBC considered the canonical mode when there are streaming modes available such as CFB and OFB? One thing that I can think of is that in CBC you can easliy do range-based decryption. All you have to do is load the previous block (whose size is explicit). How would you do it in CFB/OFB? In my previous question I ...
I've identified a weakness in a distributed simulation system I'm looking at, and I'm looking for some advice on how to fix it. Clients initially negotiate an authentication token with a login server using Diffie-Hellman. They then connect to the each simulation node they require (seperate hosts) in turn, using the tok...
I have learnt that Linear Congruential Random Number Generators are not cryptographically secure - my understanding is that given an LCG of the form: X_n = (aX_(n-1) + c) mod m It is possible to predict future X_n given a number of past X_n (even without knowing a, c, m). In most implementations however there are a co...
If you had to implement BGN, how would you do it? I'm looking for an implementation of the public-key cryptosystem due to Boneh, Goh, and Nissim (aka BGN), or at least some suggestions on implementing it myself. My goals are to explore/learn/play around with its structure, and, eventually, to produce some kind of timin...
Constructing a hash tree is simple enough if the data fits into a number of blocks that is a power of two. root = H(H(A+B)+H(C+D)) / \ H(A+B) H(C+D) / \ / \ A B C D In other cases, there is some flexibility. The missing blocks could be repl...
I've looked at several hash function specifications, and they all emphasize the need for big-endian byte ordering. Is there a reason for this that has to do with security, or is it simply convention?
Let's say I have two keys K1 and K2. two messages M1 and M2 of the same length. Cipher (E,D) 3 ciphertexts: C11, C12,C22 where Cij = E(Ki, Mj) In situation where attacker knows K2 and all the ciphertexts (which also gives him M2), can I choose a cipher to guarantee that attacker won't be able to compute neither the...
I just learned that the THEX hash tree specification which is widely used in P2P requires that two different hash functions be used: one for the leaf nodes (hashes of input data) and one for the internal hashes (hashes of hashes). In order to protect against collisions between leaf hashes and internal hashes, differ...
I am trying to understand the notion of RSA security. Choosing a public exponent where $e = 3$ facilitates the calculations, considering that it is secure if the plaintext or message is long. If the message is short, it affects security but why? Does that relates to the $2^n$ possibilities, if the message is short the ...
Consider the following fixed length MAC for messages of length $\ell(n)=2n-2$ using a pseudorandom function $F$: On input of a mesage $m_0||m_1$ ($|m_0| = |m_1| = n-1$) and a key $k \in \{0,1\}^n$, algorithm Mac outputs $t=F_k(0||m_0)||F_k(1,m_1)$. Algorithm Vrfy is defined in the natural way. Is (Gen, Mac, Vrfy) exist...
I'm planning on using this Javascript BCrypt implementation, but as you can see in the code, it uses a 4KB precalculated dataset for the P and S parameters needed for blowfish hashing. I've also tracked a similar dataset back to the original C BCrypt code. Shouldn't blowfish hashing use a dynamically calculated dataset...
Say I want to verify the identity of Alice, but Alice could be colluding with Bob to fool me. Is there any way to verify Alice's identity and also be sure that Bob is not impersonating Alice, e.g. using her private key?
Let me ask whether SHA1 is designed to be secure for the following case. You compute each SHA1 of many strings,for example 1 million, where each string is a concatenation of X+Y , where X is secret and constant and Y is public and variable. Thank you in advance.
In DES, different S-boxes were tested for cryptanalytic resistance and the most secure one was chosen for the algorithm itself. How do different S-boxes offer different levels of security against cryptanalysis and how is this tested?
Under the assumption that there exists a real-world implementation of the McEliece scheme, could it be applied to streaming data as is? By that I mean in 'block cipher mode'? I've read that McEliece is very fast in encryption and decryption, hence calculating a session key for a symmetric stream cipher might be unneces...
When using the RSA cryptosystem, does it still work if you instead encrypt with the private key and decrypt with the public key? What about in the case of using RSA for sender authentication?
Given a binary shift register of $n$ bits, a primitive binary nonlinear feedback shift register will generate a sequence with a period of $2^n - 1$. While I am unable to find a paper which directly describes the methods, the paper A List of Maximum Period NLFSRs has just came up on eprint, which lists all NLFRSs with a...
In my application I'm doing a DH key exchange, where both sides generate their own ephemeral key. No static keys are used. I am trying to make my application resistant against an active attack and therefore need to validate the public key that my counterpart is sending me. Below I'm using standard DH variable names: ...
I'm building a storage system for JSON documents where they are looked up on a 128 bit key. These JSON documents have a timestamp within them, but apart from that are user-entered data. These JSON documents can have within them private information, so I want to avoid any issues where two documents have the same hash an...
I want to encrypt a key file, which is assumed to be truly random (generated with hardware RNG, for instance). Given that there are no patterns in the plaintext, what implications are there for my choice of encryption algorithm? Could I get away with something as trivial as a Vigenere cipher (or XOR equivalent)? Assumi...
Lets say you are presented with an encrypted string of bits or text, and no other information. What would be necessary before you could apply brute force methods to decrypting the string? How would a cryptanalyst approach such a case? (lets assume the conditions are such that the encryption can be brute forced in a rea...
To authenticate a message $m = m_1 \,\|\, \dots \,\|\,m_n$ the tag $t := F_k(r) \oplus F_k(m_1) \oplus \dotsb \oplus F_k(m_n)$ is used, where r is uniform random number $(0,1)^n$ and $m=(0,1)^n$. Even though the random number is prepended to the sequence there is still a chance of reordering the message blocks which ma...
As evident from the site of john the ripper, JTR example, john can be used for finding password form a unix machine passwd file. can JtR be used to crack password of a password encrypted word file? I know there is another utility by openwall which does the same...
I'm using the SHA1/2 family of algorithms for a particular project. I was wondering if all the SHA algorithms return a fixed length hash regardless of the length of the data.
How can I ensure order of encrypted data i.e., Enc(m1) < Enc(m2) where m1 < m2, and all messages are integer values. I have gone through Order Preserving Encryption discussed in Enabling Search over Encrypted Multimedia Databases. According to the literature, for sorted data values (i.e., words), lower limit (l_w) and...
I'm implementing the Secure Remote Protocol that is specified to have this equation for the parameter S, the premaster secret. S = (B - (k * g^x)) ^ (a + (u * x)) % N But the implementation I'm referring to, has done it this way. Is this equivalent to the author's description? Its too complex for me to understand. Ca...
Suppose I have a cryptography library that provides me with a black-box random number generator that is supposed to be suitable for long-lived key generation. (Under the hood it may be assumed to use some combination of /dev/random or equivalent, and stretching with a CSPRNG.) I would like to write a unit test that ca...
I'm deploying a secure remote password protocol implementation and I'm wondering what the consequences are when the client generated verifier gets leaked to an attacker. I've read Thomas Wu's paper and as nice as it is, it doesn't talk about that scenario. I also read RFC 5054 and it has the assertion: If an attacke...
I have a block of data crypted using twofish with a key of 128 bit. The data must be accessed from a GUI, the user gives the key, the block is decoded and the real data is accessed. Problem is that I need to be sure that the key is correct before trying to decode the block. My current solution is to have a file (say c...
Suppose you have an infinite list of random bytes, and you select the first N bytes that correspond to printable ASCII characters. Is this list of N bytes still as secure (e.g. for the purpose of a crypto secret or salt) as accepting all of the bytes (printable ASCII or otherwise)? I am basically asking whether this co...
I have the following question: What polynomial, when factored over the field $GF (2^8)$ based on the irreducible polynomial that is used in Rijndael, will factor into all the polynomials in the field? As I understand it, the polynomial should be an irreducible polynomial and this polynomial must factor all the polyno...
I'm working with a server/client system that has securely negotiated a private key. I need to encrypt/decrypt messages passing in both directions which are typically between 100 bytes to 100 KB. I'm working with AES-128 bit, but I cannot really understand how the private key is to be used with the encryption algorithm....
I'm looking for some PRNGs and – as I have been using Java for a long period of time – I thought that the BitInteger class, together with the Random class, could both generate some large pseudo random numbers. Are the algorithms behind those generations cryptographically secure, or is it just some sort of a + (b - c) ...
As explained in William Stallings' Book, in PGP encryption is done after compression, since it reduces redundancy. I couldn't relate encryption strength with redundancy. Could anyone explain more on that?
I am confused about how long a stream cipher can be used before you should change the key. To be concrete, let me use the stream cipher based on RC4 as an example. Let's say I want to encrypt a very long message. I pick a key with 128 bits and start encrypting using the RC4 stream cipher. How many rounds does RC4 have ...
I'm looking for an encoding scheme that requires a very large encoding key E (>10MB) and suffices with a relatively small decoding key D (<4kB). One should be able to prove some lower bound on |E| using only knowledge about the scheme, the encoded message and D. It would be great if the proposed scheme has computation...
I'm using the Paillier cryptosystem in a protocol similar to mental poker. In the beginning of the protocol, each player generates a Paillier public key $(n,g)$. Later in the protocol, a player may reveal any message encrypted by his public key (by revealing both the message and the randomizer used). The other players ...
I want a way to encrypt files using this process: https://crypto.stackexchange.com/a/15 . That is: generate a random password, use that to AES-encrypt a file, and use an RSA public key to encrypt the random password. I can arrange for the password (= AES key) to be randomly generated every single time, and can arrange ...
I am making an arduino project to open my garage door. I want to make it so users with the passphrase can open the door. Due to computational restrictions it is unlikely encryption is possible. Under the assumption that only hashing algorithms are available, what is a secure way of protecting the door? My thoughts:...
In compressed form, ECDSA public keys are one bit larger than the curve size. There are some situations where this extra bit is extremely inelegant. So I had the following idea as a way to remove it. For a public key, the extra bit is always zero and so does not need to be sent. If a private key produces an extra bit ...
I want to use the improved sha1 hashing algorithm from the Intel blog described here Intel sha1 hashing. Currently I am using Openssl sha1 hashing in my application. I wanted to know if anybody has used the Intel sha1 hashing and how does it compare against Openssl implementation as far as performance is concerned? Al...
Imagine a Wi-Fi network protected by WEP/WPA/WPA2. Users can join the network in case they know the pre-shared key of the access point. Is it possible for a user A (who has successfully logged into the network) to sniff on the data communication of another user B, entirely because A uses the same pre-shared key like B...
Suppose you need to authenticate yourself to a program with the password - but the program's source code is public, the program doesn't have access to any private information and all your communications with the program are public. The only privacy you have is the information that you have but don't send. No fixed pas...
There are several papers about Secure Indexes, for Example "Searchable Symmetric Encryption: Improved Definitions and Efficient Constructions" and "Secure Indexes". I'm trying to build a system, that uses secure indexes to store and search data. Are there any existing solutions out there which implement these types of...
A comment on another question made me wonder about something: Assume you're on a rather constrained platform — say, a low-end embedded device — with no built-in crypto capabilities, but you do have access to a simple stream cipher; say, RC4 or one of the eSTREAM ciphers. What other crypto primitives can you build out...
This mode is that each time a random number $K$ is generated, you XOR it with plaintext $M$ and then pass the result to AES. Since AES is a pseudo random permutation, does AES have the following property? $$AES(M \oplus K) = AES(M) \oplus AES(K)$$
HMAC-based One Time Password (HOTP) was published as an informational IETF RFC 4226 in December 2005. In May, 2011, Time-based One-time Password Algorithm (TOTP) officially became RFC 6238. What advantages does it introduce?
First up: it's a step in some challenge found on the Internet, where we get an application and a file. The application must be feed with that file and a password (the password is the flag for the challenge). So, after reversing the application, I found that the algorithm used is RC4 with a small change in the "S" array...
I am writing a small program which uses AES. In testing it with wrong passwords, I get error prompts from Microsoft C# component saying "the padding is bad"; whereas I expect wrongly decoded texts. Do these errors come from the original AES spec or not?
Background In both, bitstrings are interpreted as a polnomical over GF(2) and they each can be used to implement a hash over a sliding window. The definitions of each are as follows: Rabin Fingerprint: $M(x) = Q(x) \cdot G(x) + R (x)$ CRC: $M(x) \cdot x^{n} = Q(x) \cdot G(x) + R (x)$ Where $M(x)$ is message polynomial,...
In order to guard against denial-of-service attacks, I want to require clients to do some work (more work than the server does fulfilling the request) before talking to them. Client connects Server sends a challenge, including a piece of data "Find bytes x such that hash(challengeData + x) has n zeros at the beginning...
At StackOverflow, this question has been asked. It uses additional random entropy and a hash method (among others) to try and create a cryptographically secure pseudo-random number generator for PHP. PHP seems to use a Mersenne Twister algorithm with a large internal state and high period, but Wikipedia assures me that...
I've been trying to implement the Paillier Signature Scheme in Delphi, but I can't get it to work and I don't know where the problem is. First of all, I got my info about the scheme from this paper. The signature scheme is on page 9. The problem is that the signature is never valid according to this code. It's either t...
My question might appear the same as the question Taking advantage of one-time pad key reuse?, but actually I did read all the answers and none of them helped me with the details I need. I am new to cryptography and my problem is with two time pad attacks on OTP. The problem I had in my course was that I have 10 cipher...
The cipher AES-256 is used among other places in SSL/TLS across the Internet. It's considered among the top ciphers. In theory it's not crackable since the combinations of keys are massive. Although NSA has categorized this in Suite B, they have also recommended using higher than 128-bit keys for encryption. So how sec...
If a pseudo-random sequence generator is built so that it uses an n-bit seed and outputs a string that is of length x. Let's say one wants to generate a bit string of length y and uses the previous PRSG over and over to obtain y bits out of the x bits produced per run. In order to stop repetitions the last n bits of ea...
Is anyone able to point me towards a known-to-be-good diffie-hellman group? I currently use group 24 (RFC5114, 2048-bit MODP Group with 256-bit Prime Order Subgroup). It came to me that this group is not adequate even for AES-128 (this is according to www.cryptopp.com/wiki/Diffie-Hellman)...so far it seems my only opti...
It seems like the pre-master secret generated during the SRP protocol would make a good source to generate a shared private key using a secure hash to compress it down into a 128/256 symmetric key. The random values that get hashed into it seem to make it good for that purpose.
One of the methods to break a ECDLP is Pollard's rho algorithm. When ECDLP is defined over a finite field $F_p$, and given a relation $S=w.T$, where S and T are a member of $F_p$. Then ECDLP is to find w. The algorithm is supposed to take a time $O(\sqrt p)$. The authors say its exponential or subexponential, at best. ...
I understand the basics of OTP: $|\text{key space}| = |\text{plaintext space}|$ implies perfect security, key reuse destroys this. Cryptanalysis on the $N$-Time Pad for $N > 1$ involves finding patterns in the ciphertext; this, however, all seems based on the premise that patterns exist in the plaintext (e.g. English l...
I know the basic differences between Symmetric vs. Asymmetric cryptography, but I'd love to know more details: Exactly why is the asymmetric approach slower than the symmetric? Why does it make use of longer keys? Why does it require more processing power, etc, etc? In what ways does it trump the symmetric approach...
Background: I've been thinking about using encryption in the context of backing up files to untrusted locations (to the point of making the file publicly and widely distributed for practically failsafe backup). The problem is, once a file is publicly available, it will forever remain so. And in 20 years, when comput...
The scenario is single-use passphrase-based non-interactive message authentication. The obvious try to do this is to chose a random salt of the appropriate length and send: concat(workfactor, salt, message, mac(scrypt(workfactor, salt, passphrase), message)). That protocol is as secure as scrypt is a non-mallea...
The initialization vector (IV) is exclusive or'd against the plain text before encryption for the first block sent in order to prevent an attacker from learning that duplicate message blocks are being sent. This technique is often used with streaming modes like CBC. I have researched some of the questions that were as...
I was wondering, whether there exist such algorithms/enciphering procedures which both compress and encrypt the input data. That means, for starters, the output will be both smaller in size and difficult to decrypt...and if the compression algo is good, then the bits will be almost random. Also any twin-encryption alg...
One use of an anti-forgery token is to prevent Cross-Site Request Forgery (CSRF) attacks. The attacker doesn't need to sniff the wire in order to carry out a CSRF attack. This attack relays on the fact that the HTTP request is predictable, and the defense is to add a secret value such that an attacker cannot forge ...
I a have a question about PRNGs and this is my very first experience with them. I have the following generator that takes a 56-bit seed $p$ during initialization and then chooses both $X$ and $Y$ randomly from the interval $[0, p]$. Every time it is called, it returns the output of the next function: def next(self): ...
I have a very basic doubt in RSA key generation and its usage. In RSA key generation you choose two large prime numbers of a very large order. Then you multiply them.(eq $p \cdot q = N$) Now, $\phi(N)=(p-1)(q-1)$. Now you find a number $0 < e < \phi(N)$ such that $e$ and $\phi(N)$ are coprime. {$e,N$} becomes your publ...
I'm using twofish. Say you have a 120 bit key, is there any difference in using a 128 bit bit keylength or a 256 bit one? Since the most significant digits of the key will be allo zero in both cases, does the keylen parameter really matter?
I have a 512 bit master key, and 128 bit unique identifiers. I'm going to derive 256 bit keys to for use with deterministic and block ciphers. For reference, The KDF I'm going to use is Hash( C | Z). The implementation will be SHA256( uuid | master key). I don't particularly care if SHA256 generates collisions ...