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Suppose both I and my friend have a set of integer numbers. We want to know the number of common elements in our two sets but without knowing elements of the sets of each other. So I don't want my friend to know any element of my set and he don't want me to know his. But we want to know how many elements are in the int...
The Alternating Step Generator (ASG) is a PRNG combining 3 LFSRs. Output of the ASG is the XOR of the output of two clock-gated LFSRs. At each step, a single one of these LFSRs is clocked, according to the output of the control LFSR. The best (AFAIK) claimed attack on the ASG is Reduced Complexity Attacks on the ASG (S...
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: Both parties hash the master password using SHA-256 to create a password hash. The password hash is used by the client to encrypt a message which inclu...
When a user wants to communicate with another user (let's say Alice and Bob), what is sent over the network during the initial communication? Alice uses her Kerberos client and enters her password and username. Something which is not clear to me: Will she send a message containing time username hash of password gene...
The goal of the Tahoe-LAFS 100 Year Cryptography project is to "enhance Tahoe-LAFS's cryptographic system so that Tahoe shipped today/next year might remain safe from cryptographic attacks for a 100 years." Its developers are openly collaborating knowledgeable experts in the field, with at least all the information on...
Currently I'm implementing a PRNG for an embedded system. Using the RFC 4086 I've decided to use the X9.17 - to be more specific the successor X9.31- standard to implement my PRNG. X9.17 uses DES, but X9.31 uses AES! Now I need to specify the value of the AES key for X9.31. I know that at least my AES key must be unpr...
I'd like to create an encrypted file that: Can be decrypted on a variety of platforms (mainly Windows, OS X, and Linux) with knowledge of the key. Can be decrypted with existing tools (perhaps writing a shell script piping together common tools). Is in such a simple file format such that it'd be relatively easy to w...
If Camellia is of equivalent security and speed to AES, concerns arise. First of all, assuming the above, why is Camellia so rarely used in practice? Why aren't there any breaks in Camellia? Does that mean that Camellia is currently more secure than AES, or is this a result of the lack of research on the cryptanalysis ...
I'm reading that AES uses 4x4 bytes (448 = 256 bits key) matrix for performances matters (since it's a requirement for common standard encryption algorithms), but are there implementations with choosable key size for this particular algorithm, so I can make brute-force attacks harder with a good password ? Also, if I...
I don't yet perfectly understand the difference between brute-force and dictionary attack since this differentiates one attacking the key and another attacking password: apparently attacking passwords can take longer, right? But it's not necessarily true depending how unaware users can be, and that's where dictionaries...
Is combining digests (created using a hash function) using arithmetic addition, and then hashing and publishing the result, less secure than publishing the set of digests? Does the answer change if the outer hash function is different from the inner function? I am working on a proposal for Bitcoin to enable m-of-n sign...
I have a scenario similar to the one described in Wikipedia: hash list, but with a twist. I'm looking for a cryptographically secure hash function that would create the same root hash for the same file, no matter how the the file is chopped up for the individual hashes in the list. E.g. case 1: File is divided into 3 ...
Post-quantum cryptography concentrates on cryptographic algorithms that remain secure in the face of large scale quantum computers. In general, the main focus seems to be on public-key encryption algorithms and public-key signature algorithms - but there are dozens of other constructs like hashes, block ciphers, etc. -...
If I have a message M and a public key P, and I encrypt them alongside one another: CIPHER = AES(M + P, aes_key) Is CIPHER now weakened if someone knows what P is? It seems like if I encrypted only P: CIPHER = AES(P, aes_key) that it should be possible to recover aes_key from CIPHER. I realize that this is different ...
Suppose I want a strong 20-bit blockcipher. In other words, I want a function that takes a key (suppose the key is 128 bits), and implements a permutation from 20 bits to 20 bits. The set of permutations should be close to a randomly-chosen subset of size $2^{128}$ of all $2^{20}!$ permutations on 20 bits. I don't wa...
A recent approach to creating a decentralized online currency, called Bitcoin, has been generating some interest. The goal is to have a way to transfer currency without a central authority and without double spending or counterfeiting. Their approach is to have all the nodes in the network try to verify a transaction b...
Linear and differential cryptanalysis seem well suited for constructs with a (relatively) simple fixed structure of boolean expressions. But some ciphers incorporate swaps of array elements where the indices to be swapped are dependent on dynamic cipher state and others may include rotations by a variable number of bit...
If a researcher manages to make a cryptanalytic breakthrough on a cryptographic algorithm or protocol that is in use, what should they do? Has this ever happened before? What are the implications for release and how do those relying on such systems ensure they are not caught in a situation where the crypto-system on wh...
[I was torn between posting here or security.stackexchange.com. In the end, I felt that this was more of a design question, rather than an implementation question and so chose this forum.] My question is: How do I assure myself that the results data submitted to me was generated by my official build of an open source p...
I heard that there are 128 stochastically independent bits in an MD5 output. Is that true? If so, are there any citations or proofs for that?
My understanding of hashing and encryption is rather limited. I certainly do not understand the mathematical formulas at play in these algorithms. With that said, what part do prime numbers play in cryptography? When I was in college, one of my professors told me that the fact that there is no formula to predict a prim...
I am interested in exploring ECC implicit certificates, specifically using the ECQV protocol. While the actual implementation would not difficult to perform using building blocks provided by most ECC capable libraries, I really would like to compare my application with a reference implementation. Does anyone know of a ...
In my question "Authenticating data generated by a particular build of an open source program", Dave Cary requested that I post a question stating my real problem on a high level rather than the partial solution and abstract approach I took. So here goes: Need to develop a program that collects raw scores at a competit...
Are there any ongoing or current practical attempts to solve instances of the discrete logarithm problem of the order of magnitude used in cryptographic applications, for example with a 256 bit modulus and 160 bit exponent? I am interested in efforts similar to the work of members of the Mersenne Prime forum and the R...
For a certain application I need a commitment scheme where each user could make a commitment, and a single verification operation could verify all the commitments simultaneously, faster than single verifications. It's like a batch verification of signatures but we are able to build each commitment based on the previous...
When I read about a choosen plaintext attack, for example on AES the block size is always 128 bits, does it mean the attacker will only supply 128 bits data words as "plain text" ?
I'm looking for a scheme where signing may be costly (slow) but batch verification with different signers is the fastest possible. Modified ECDSA allows batch verification for different signers with a 4X speedup [1]. Is there any signature scheme than can do better? [1] Fast Batch Verification of Multiple Signatures. J...
There are several well-known techniques to generate pairing-friendly curves of degrees 1 to 36 on prime fields GF(p): Cocks-Pinch, MNT, Brezing-Weng, and several others. In extension fields GF(p^n), however, one is confined to supersingular curves. In characteristic 2, embedding degrees are <= 4, and in characteristic ...
I have a use case where I need to encrypt some text in the browser using javascript. Only the encrypted text will be stored on the server. The user should then be able to take the encrypted result and decrypt it with GPG on the command line. I want to use GPG as it's easily available and the AES appears to support iter...
From FIPS 180-3 Suppose that the length of the message, $M$, is $l$ bits. Append the bit $1$ to the end of the message, followed by $k$ zero bits, where $k$ is the smallest, non-negative solution to the equation $l + 1 + k \equiv 448 \mod 512$ . [...] For example, the (8-bit ASCII) message “abc” has length $8 ...
This is more of a research question. I was wondering what types of crypto algorithms would work best on a small 4-8 bit micro controller. I recently read a paper called Security Considerations for 802.15.4 Networks and was wondering if anyone out there can think of any other papers or has knowledge about what types of...
I was reading on a site about the Zodiac Killer and how he used a basic substitution cipher, but instead of substituting english letters and characters he substituted symbols. I was wondering, if you had a large enough subset of symbols to use for commonly repeating letters like E,T,S ... then by what means could someo...
I have read in Applied Cryptography that the NSA is the largest hardware buyer and the largest mathematician employer in the world. How can we reason about the symmetric ciphers cryptanalysis capabilities of code-breaking agencies like the NSA or GCHQ given that they have performed first class unpublished cryptograph...
The Feige-Fiat-Shamir identity scheme is based on a ZKP assuming that square roots are "hard" modulo an integer of unknown factorization. The "parallel version" of this protocol includes a "sign bit" and the wikipedia article claims that the older version of the protocol leaked a bit, so the sign bit was added. Here ...
I'm currently reading Cryptography Engineering. After giving a high level explanation of the difference between secret-key encryption and public-key encryption, the book says: So why do we bother with secret-key encryption if public-key encryption is so much easier? Because public-key encryption is much less efficient...
I'm planning to encrypt some individual files for storage, using the GnuPG implementation of RSA. If I happened to encrypt the private key corresponding to the public key used for encrypting -- either as an internal GnuPG file or an ASCII-armored exported key -- would this constitute a vulnerability? The key in questio...
RSA, DES, AES, etc., all use (relatively) complicated mathematics to encrypt some message with some key. For each of these methods, there have been several documented vulnerabilities found over the years. Some even believe that there is a vulnerability in AES known only to the NSA. On the other hand, the one-time pad i...
Does there exist any cryptographic algorithm which encrypts data in such a way that it can only be decrypted after a certain period of time? The only idea that I can think of, is something like this: Seed a PRNG with a public value. Run the PRNG for a week and use the final value it produces to encrypt the message. Now...
In some text I am reading, there is an exercise asking to show that KeeLoq decryption function is the inverse of the encryption function. Details about KeeLoq are given in the Wikipedia article. As I am no hardware guy, I have no clue how to approach this problem. Does someone happen to see, how to show the requested p...
I'm trying to create a ISO8583 Rev93 message. What is the standard way of generating MAC key in ANSI X9.9 DES-CBC encryption algorithm is used to encrypt the message and generate the MAC. How many bytes should I take from the encrypted byte array based on ANSI X9.9 standard? 8 or 16? I think I should take 4 bytes (8...
I know it uses RSA/DSA to create keys, but does it use that same algorithm for the actual cipher?
The NTRU public-key cryptosystem has a lot of interesting properties (being resistant to quantum computer attacks, being standardized by several important bodies), but it also has a pretty unique property: The decryption algorithm does not always work. Sometimes it just gives wrong answers. Has this been fixed? Is ...
My application can authenticate via openid and oauth (facebook, twitter, etc) and also with its own authentication system. I previously switched hashing from MD5 to SHA1 and during migration I had to customize so that accounts could verify both with MD5 and SHA1 and now I've removed the MD5 completely. I read here som...
Craig Gentry recently gave the first fully homomorphic cryptosystem. Quite a bit of work has been done since extending his work. It seems, however, that no system is practical for real world use. What are the current roadblocks making FHE impractical? Which proposed system would you say is currently the most practical...
I stumbled upon this question in some textbook. Propose a variant of ElGamal signature scheme such that there is no need to calculate the inverse $k^{-1}$ as it is usually done using the EEA. Recalling what ElGamal signature is about: we fix a prime number $p$ and a generator $\alpha$ of $Z_p^*$. User $A$ then choo...
What is the exact purpose of the date/time vector $dt$ in the ANSI X9.31 PRNG? $$ I := E_K(dt) $$ $$ R := E_K(I \oplus V_{old}) $$ $$ V_{new} := E_K(R \oplus I) $$ Specifically, the document seems to imply that the seed $V_*$ and key $K$ must be kept secret, but makes no claims on the secrecy of the $dt$ vector, only...
For the Diffie-Hellman protocol I've heard that the generator 3 is as safe as any other generator. Yet, 32-bit or 256-bit exponents are sometimes used as generators. What is the benefit of using these very large generators if they are just as safe as the generator 3? If 3 is not the safest generator, how could one cal...
When a user on facebook grants an app access to their account, an API key is issued to the app. This key is app and user-specific. This process is described in Facebook's developer documentation. Until recently, API keys could be parsed- they contained the app's numeric ID, the user's ID, and other information (timesta...
This question is related to ElGamal signature scheme as defined here ElGamal signature without calculating the inverse Show how one could exploit an implementation ElGamal signature scheme in which it is not checked that $0 \leq \gamma \leq p-1.$ As far as I can see, we have to find a $\gamma$ such that $\alpha^{a\gam...
I am aware of the vulnerabilities of simple xor ciphers and recently I came across a block cipher that claims to solve those vulnerabilities. The cipher goes as follows with both the block and key sizes at 256-bits: the key is separated into chunks of length 1 bit. Every bit in the plaintext is xored with every key ch...
I was studying DSS from "Cryptography and Network Security" by William Stallings. What puzzled me was the DSS approach figure described in the text. It says it uses Public and Private Keys for creating signature. But the algorithm for creating signature in DSA doesn't use it. $$r = (g^{k}\mod p)\mod q$$ $$s = (k^{-...
I have been studying Elliptic Curve Cryptography as part of a course based on the book Cryptography and Network Security. The text for provides an excellent theoretical definition of the algorithm but I'm having a hard time understanding all of the theory involved in ECC. I'm looking for an explanation suitable for som...
This question is a companion to the equivalent question on elliptic curves. Preliminaries Diffie-Hellman, Elgamal, DSA, etc. are examples of protocols that work in the integers modulus a large prime $p$. However, for security reasons, we do not use all the integers in $\mathbb{Z}^*_p$ but only a subset of them. The sub...
I would like to generate a 256-bit hash on a microcontroller that has a 128-bit (only) AES engine. How can I construct a 256-bit hash function from a 128-bit cipher?
I have a Truecrypt container which I want to synchronise between computers (i.e. different people, that I want to share the data with). If I used Dropbox for synchronisation and someone downloaded all the different versions of a publicly accessible Truecrypt container over time, whenever it gets changed, is it then eas...
I'm looking for information on the MJH double-block-length hash function, but the best free source I could find is the diagram on page 18 of Efficient hashing using the AES Instruction Set (submitted to the ECRYPT II Hash Workshop 2011). Is source code available for this function? What are the standard symbols used (M,...
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). Q...
I'm looking for best practices when it comes to encrypting small (< 128 bytes) amounts of data with the RSA private key. Signing it would make the resulting payload too large.
I'm investigating this function: $a := ((b\cdot c) \bmod k) - (b \cdot c)/k$ where $/$ indicates integer division. Two things I've noticed: It's equivalent to multiplying a·b, and then subtracting the high digits from the low digits (in a radix which divides k) It's completely linear and can be inverted (that is, gi...
Please forgive the impracticality of this question, but I'm curious about the behaviors of encryption algorithms applied to their own output. Suppose I have an encryption algorithm E and (using the same key(s)) I repeatedly encrypt its output for a given plaintext: E(E(E(E(...E(plaintext) Would a modern encryption algo...
Say I want a random 1024-bit prime $p$. The obviously-correct way to do this is select a random 1024-bit number and test its primality with the usual well-known tests. But suppose instead that I do this: select random odd 1024-bit number $n$ if $n$ is prime, return $n$ $n \leftarrow n+2$ goto 2 (This approach allows...
I am attempting to duplicate wireshark's packet capture decryption for a TLS HTTP session, where I control the private key of the server. The cipher suite number is 0x00002f, TLS_RSA_AES_128_CBC_SHA I wrote a utility that takes apart the packet captures using libpcap, and so far can match what the logs from wireshark s...
I'm working on a cryptosystem which uses IDEA. The designer made the mistake of including a CRC-32B hash of the password unencrypted in the header, so that the system can quickly reject bad passwords. Of course, that opens it up to the obvious attack of brute forcing CRC32 over potential passwords until the right one...
There are zillions of articles describing CRC. What can I read to (more deeply) understand what's really going on? Both from an algebraic perspective and a bit-manipulation perspective, I'd like to understand it well enough to have an intuitive feel for it. (Also see Brute forcing CRC-32 )
When bruteforcing a password (e.g. the common attacks on DES), where you have ciphertext only, you need a way to assess whether a decrypted plaintext is the right one. I believe the EFF DES machine does this by checking if the chars are printable. Of course, this only works for ASCII files, not things like images. I'...
Most CS/Math undergrads run into the well-known RSA cryptosystem at some point. But about 10 years ago Boneh and Franklin introduced a practical Identity-Based Encryption system (IBE) that has excited much of the research community and produced a huge flood of follow-up work. What is IBE exactly and in what way does i...
Underlying the Schnorr signature is an identification protocol: let $G$ be a cyclic group where discrete log is "hard" and choose $g$ as a generator of $G$. Now have Alice pick a random (secret) exponent $s$ and publish $v=g^s$. To identify herself to Bob, it goes like this: Alice chooses a random exponent $r$ and s...
The well-known Counter-Mode (CTR) mode of operation for a block cipher essentially converts any block cipher into a stream cipher. Is there a way to do the reverse? In other words, given a "good" stream cipher $G$, can we construct a block cipher that builds its strength based on $G$?
Working on a cipher (which I assume to be a mono-alphabetic substitution cipher due to the letter frequency) I struggle with the fact that I don't know which language the plain text is written in. Looking at the letter frequency only, gives some hints, at least to exclude some languages, but far from pointing out one. ...
I understand the use of pseudo-random number generators. I am not getting mixed up between these and "real" random number generators. However, I don't understand for what a real random number generator is used. If it is not deterministic, how can it be used in an algorithm?
Recently a company called Bitcasa demonstrated a product of cloud storage. they indicated that they would use "Convergent Encryption" to secure your data and de-duplicate, essentially one copy of the same file between users. From what I can read on a university paper about Secure Data Duplication which makes mention of...
Why use an Initialization Vector (IV)? How are IV's used? What are the advantages/disadvantages of using an IV? Why use an IV instead of a longer key in which some section of the key is public? What happens to various security properties if an IV is insufficiently random? Are IV's always public knowledge? If so is thi...
I have a program where computing SHA-1 is the bottleneck. This is using OpenSSL 1.0.0e on a 2.6Ghz 16-core Opteron where I get about 325MiB/s throughput. (SHA1 here is via Andy Polyakov's x86-64 assembly implementation using SSSE3.) If I need to go faster, what makes most sense? Use multiple cores Use another implem...
Inspired by "Guarding against cryptanalytic breakthroughs: combining multiple hash functions", I am curious if there is a cryptographic reason to use only one algorithm during encryption. For example, start with Blowfish, move to AES, switch to DES, etc, in a defined, but semi-unpredictable fashion (maybe basing which ...
Is it possible to compose or combine $n$ ciphers ($cipher_0, cipher_1, ... cipher_n$) in such a way that they generate $n$ ciphertexts from the same key, $k$, and that recovering the key, $k$, from the $n$ ciphertexts is equivalent to breaking all $n$ ciphers. Note that the size of the key, $k$, is the same as the siz...
Consider the following (probably naive) scenario. Alice, who is very limited in her knowledge of security in general (clueless about securing a private key for example), wishes to delegate certain contractual operations to Trent, an apparent trusted expert in that field. However, Alice is rightly cautious and is of th...
I have a ciphertext generated by a classical cipher. I do not know what was cipher used to generate it. I do however have the beginning of the plaintext. What are the cryptanalysis approaches for classical ciphers? How do you suggest trying to recover the plaintext in this instance? How can I leverage the known plai...
Suppose that a single evaluation of a block-cipher (DES or AES) takes 10 operations, and the computer can do $10^{15}$ such operations per second. How long would it take for to recover a DES key, using a brute-force search? How about a 128-bit AES key?
Is the following statement true: If $G: \{0,1\}^k \to \{0,1\}^n$ is a PRG, then so is $G':\{0,1\}^{k+l} \to \{0,1\}^{n+l}$ defined by $$G'(x\|\|x')=G(x)\|\|x'$$ where $x \in \{0,1\}^k$ and $x' \in \{0,1\}^l$ (where $\|\|$ denotes concatenation). My thought is that since $x'$ is not processed through the pseudo number ...
Is there any way to effectively generate valid distributed public key in schemes like ElGamal or Benaloh for a number of participants? There's no need in private keys since there's no intent to decrypt messages at all, only to encrypt them securely. As far as I know, there's no effective way to generate distributed key...
For security's sake, of course it's blasphemous to store passwords in plain-text; using a hash function and then doing a re-hash and comparison is considered much better. But, if bad guys steal your database, they still could brute-force against the hash and conceivably retrieve many passwords. The question I have is: ...
I am looking for a hash function that is computable by hand (in reasonable time). The function should be at least a little bit secure: There should be no trivial way to find a collision (by hand). For instance, a simple cross-sum is not meeting this criteria since one can easily construct a number with the same hash th...
Several people are playing a game with random events and require a way to produce a random number. (Such as dice rolls or a lottery.) Can this be done such that each player has the power to be reasonably sure that the random number was fairly selected, without having to trust anyone else? This question stems from a dis...
Assume there is a public-key encryption scheme $(KeyGen, Enc, Dec)$ with perfect correctness (i.e., for all messages M and valid key-pairs (PK,SK), we have $Dec_{SK}(Enc_{PK}(M))=M$). Will there always be a function $A$ such that for all messages M and valid public-keys PK, $A_{PK}(Enc_{PK}(M))=M$? In other words, can ...
In the original paper introducing RSA, it is implied that one should first choose $d$ and then calulate $e$ from $p$, $q$, and $d$. However, I have found in other places (such as the wikipedia article on RSA) that one should first calculate $e$, and only then calclulate $d$ from it. Which of these two methods are prefe...
Over on the bitcoin forums I asked why the bitcoin client computes SHA-256(SHA-256(x)) as its cryptographic hash for a variety of purposes. The leading theory--since the bitcoin author has disappeared--seems to be that from a security standpoint it could be sort-of analogous to upping the number of rounds in SHA-256 fr...
Considering a cryptographic hash, such as MD5 or SHA2, denoted by the function $H(m)$ where $m$ is an arbitrary binary string, there is a lot of material available that deals with potential weakness to preimage attack. I am interested in resistance to preimage attack where the cryptographic hash is applied recursively ...
Are there any available test cases for testing elliptic curves like secp256k1 (Korblitz curves from http://www.secg.org/collateral/sec2_final.pdf)? For curves like P192 there are for example those values: http://point-at-infinity.org/ecc/nisttv . Moreover, what other ways one should test an implementation of an ellipti...
I am working with golang's elliptic library. It implements functions on Weierstrass elliptic curves with $a=-3$. I need to make my own library that allows me to handle curves with $a=0$. I understand there are specific equations to use to optimally perform operations on different elliptic curves, which can be found in ...
I am familiar with concepts such as the following: PKI and CAs ID based cryptography Certificateless cryptography PGP web of trust more or less anything in basic Crypto that is taught in a college course I need to quickly understand the main ideas behind "SPKI" or (Simple public key infrastructure). The Wikipedia pa...
Suppose that in order to avoid loss in transmission, a secret key encryption scheme $(Gen, Enc, Dec)$ is modified to be $(Gen, Enc', Dec')$, such that the message m is encrypted independently three times as $Enc'(m)=(c_1,c_2,c_3)$, each $c_i=Enc(m)$. For decryption, the 3 transmitted ciphertexts are decrypted using $De...
I have a simple problem: I have a set of users' ECDSA key pairs, and say I want to encrypt them with a simple algorithm. I have access to one variable that uniquely identifies the user, so I hash it with a SHA-2 algorithm and have a string of bytes longer than each of the keys. Is it safe to XOR a key pair, or XORing ...
Is the Diffie-Hellman key exchange the same as RSA? Diffie Hellman allows key exchange on a observed wire – but so can RSA. Alice and Bob want to exchange a key – Big brother is watching everything. Bob makes a fresh RSA key pair and sends his public key to Alice. Alice makes a random session key and sends it to Bob e...
I`m currently implementing an ECDSA library based on curves like secp256k1. I would like to test it using some test vectors, like http://csrc.nist.gov/groups/STM/cavp/documents/dss/ecdsatestvectors.zip . Is there any place where I can get some vectors for testing encryption with that curve? Example vector has this stru...
I am using RSA to encrypt some data but I would like to eliminate the possibility of message replay. By message replay I mean sending a valid message multiple times to the original recipient. It is obvious that an attacker can capture a valid message without knowing its contents and replaying it. Is there any efficient...
This answer makes the claim that the Discrete Log problem and RSA are independent from a security perspective. RSA labs makes a similar statement: The discrete logarithm problem bears the same relation to these systems as factoring does to the RSA system: the security of these systems rests on the assumption that dis...
A (synchronous) stream cipher is an algorithm which maps some fixed-length key to an arbitrary-length key-stream (i.e. a sequence of bits): $C : \{0,1\}^k \to \{0,1\}^{\infty}$. This key-stream is then XOR-ed with the plain text stream, giving the ciphertext stream. For decrypting, the same key-stream (generated from t...
I am interested in understanding what the process would be if an attacker wished to attempt to decrypt data secured by common tools such as OpenPGP, Truecrypt or the like. Are there any documented records of such undertakings, or papers I can read to understand how a cryptanalyst approaches breaking an implementation? ...
In the Diffie-Hellman key exchange, one of the steps involves calculating a primitive root of a prime number $p$. How would one go about doing so, considering that $p$ could be very large? Is there some sort of algorithm or equation?
I was looking at FOAF+SSL and wondering if its possible to spoof the modulus of the browser certificate so that the FOAF and browser certificate's modulus match?

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