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I have some questions regarding aforementioned subject: Is there a EC equivalent of RSA-OAEP key transport/encryption algorithm ? Is ECIES-KEM sufficient ?
In a paper it says "In the generic group model, the PRF is adaptively secure for inputs of $\mathbb{Z}_q^n$". Maybe a stupid question, but what does "adaptively secure" mean exactly?
I've read a lot about protocols for mental poker without a trusted server, but I'm interested in the possibility of a faster, more practical protocol that relaxes that criterion a bit and "trusts" a third-party server whose trustworthiness can be easily verified (or whose cheating can be easily proven). For example, le...
At this work at section $2.2$ concerning a possible application for the BGN cryposystem the author points out that if you want to encrypt a unit vector $\overrightarrow{u_l}$ of size $l$ then the naive way is to encrypt each bit separately. And by following the idea of BGN the size of the ciphertext is reduced to $2\sq...
Assuming the following: Key is randomly generated is being used (32 bytes+) IV is also randomly generated Crypto random key generator is used Data being encrypted contains common bytes like { } and " and keys (like JSON) Which of these modes (CTR, CBC) are more appropriate for storing sensitive information? Is it pos...
I'm trying to make a PRG using the Rabin function. The code (in Java) I wrote to implement the function is: poublic static int rabinFunction(int m, int publicKey) { return (int) Math.pow(m, 2) % publicKey; } A trivial usage (using the numbers from the wikipedia link) would be: int m = 20; int pq = 7 * 11; // outp...
Is there an existing AEAD scheme such that, for inputs with the same AD and IV ciphertexts are allowed to leak whether or not their plaintexts are equal, if the scheme can process the plaintext in a streaming manner, then it is allowed to leak where different plaintexts have their first difference, and is otherwise se...
I haven't been able to find a clear explanation on this (and I'm probably just confused in general). I have the following parameters of ElGamal signatures: $p$ = safe prime $q = (p-1)/2$ $g$ = an element of $F_p$ with order $q$. $r$ = random $1 < r < q $ $s$ = private key $Y$ = public key, $Y = g^s$ My question is, ...
If have application that is sending username and hashed password to server for authentication, how would I use salt for this scenario ?
We have the following two-party protocol between Alice and Bob. Alice sends messages $m_1, m_2, \ldots \in_R \mathbb{Z}_n^*$ to Bob and Bob signs these values by calculating $v_1, v_2, \ldots \in_R \mathbb{Z}_n^*$ and $a_1 = \left( G \cdot H^{-v_1} \cdot K^{-m_1} \right)^{1/x}\ \bmod\ n$ $a_2 = \left( G \cdot H^{-v_2} ...
I am reading this example: A random oracle is an ideal object. What makes a random oracle convenient for proofs is the part about knowing nothing on the output for a given input if you do not try it. For instance, consider the following encryption scheme: $H$ is a random oracle which outputs $n$-bit values. The key...
I have eleven ciphertexts that were encrypted with the same key (which I don't know). I want to decrypt the last ciphertext. I read similar question like Many time pad attack but I can't solve my problem with their answer. I'm new in Crypto can anyone tell what can I do? I know when XOR two ciphertext (Let's assume tha...
2 hours ago I thought I had this figured out, but now I am doubting myself and want someone to validate my algorithm. I want to take a stream of k trusted random bits and convert it to groups of 5 digits in a uniformly distributed range from 0-99999. To do this I take k and truncate to a multiple of 32, let's say the ...
Say that we have a secure random number generation that outputs 32 bit random numbers, so it's output is a true random number between 0 and a MAX. What is the best way to map this random number to a defined range (say I want something random between X and Y) without loosing too much entropy?
How to prove that if a cryptosystem has perfect secrecy for a given plaintext probability distribution then it will have perfect secrecy for all other possible plaintext probability distributions? Do we have to make any additional assumptions on probability distributions (probability of each plaintext is not zero?) to ...
How do cryptography in SSH(2) work (secure channel establishment, authentication)? Does key authentication in SSH(2) protect from MitM by providing authentication and integrity and why?
Often in security proofs a certain block cipher is assumed to be a pseudorandom permutation or PRP. I wonder if this goes for stream ciphers as well, and specifically for Salsa20. If we limit ourselves to the scope of one Salsa20 block (64 bytes), being fed 64 bytes of plaintext data, is it safe to assume $Salsa20_{key...
Is it possible to deduce the plaintext block or the key, given only a Simplified-DES ciphertext block (e.g. c=01110110)? I'm reading Cryptography And Network Security, by William Stallings and I'm bit confused.
I've not been able to understand exactly the reason behind Blowfish being faster than AES. Is it dependent on the block size? Or is it processor dependent? (if Yes, then lets assume that AES accelerators are not used) I'd like to know the exact reason behind it. Thanks.
I've recently read some articles about the Interlock Protocol, Article by Ron Rivest and Adi Shamir. I'm wondering if it is possible to protect Key-exchange under Public-Key cryptography from the MITM attack by using this protocol? There's a method here.Suppose Alice & Bob has exchange their public key, but replaced by...
I am reading an article on cryptography at following location: http://www.entrust.com/resources/pdf/cryptointro.pdf Historically, encryption systems used what is known as symmetric cryptography. Symmetric cryptography uses the same key for both encryption and decryption. Using symmetric cryptography, it is safe to sen...
Assume RSA with a public modulus $N$ of $n$ bits, a small odd public exponent $e$, plaintext $M$ a random non-negative integer less than $2^m$ for some integer parameter $m$, with $M\mapsto C=M^e\bmod N$ (textbook RSA) used for encryption. Inasmuch as it matters, assume there are $2^r$ ciphertexts available to the atta...
I am taking a cryptography class on Coursera. I learned that the compression function $h(H, m) = E_m(H) \oplus m$ is insecure (even though other variants like Davies­-Meyer or Miyaguchi-Preneel are secure). Why is this compression function insecure? What is the attack? (See also Why are the Davies-Meyer and Miyaguch...
The Davies-Meyer compression function $h(H, m) = E_m(H) \oplus H$ is said to be secure. So too is the Miyaguchi-Preneel compression function $h(H, m) = E_m(H) \oplus m \oplus H$. Why are these secure? How do we know that they are secure? (Here $E$ is a block cipher with $n$-bit key and $n$-bit plaintext; $E_k(x)$ de...
I'd like to use Python's random.choice seeded with a HMAC-SHA1 tag to generate a MAC encoded in a variable set of chars. import random, hmac, hashlib, string SECRET = 'something secret' MESSAGE = 'some message' MAC_CHARS = string.ascii_letters + string.digits MAC_LEN = 10 random.seed(hmac.new(SECRET, MESSAGE, hashlib...
I know scrypt was designed to lessen the GPU/ASIC advantage. We now have litecoin as a real-world example of this. However, it hasn't worked out perfectly. Most coins are mined by GPUs, although the advantage is probably smaller than it would have been with SHA-256. I wonder how the future for scrypt and newer generat...
I have the following scenario: Archives compressed with 7z, hundreds of MiB in size GPG to encrypt the archives (binary, without ASCII armor) PAR2 to create error correction data Question 1. Encrypted archive + plain archive error correction data If I encrypt the archive, will it compromise the security of the GPG-en...
I am trying implement the McEliece crytosystem in SAGE. My question is How I will be able to choose the appropriate matrix $S$ and $P$?. I ask this because when I trying obtain the vector $\hat{m}=mS$ in $\hat{G}\hat{m} = Decoding(c)$ I get: matrix equation has no solutions, even after verify that $G$ is full rank.
We are encrypting a small positive integer (1-1000) with a constant key using AES256 encryption. We are considering two approaches to make this secure; use an initial vector (which we then need to store as well), or just prepend some junk to the integer before encryption (possibly 6 characters, this is the plaintext w...
I am very inexperienced with cryptography and would like some advice on how to store some sensitive information on client machines. I have some information stored in a central database on my server. A snapshot of this database is distributed along with my application. Every time the application is opened on the client,...
Looking at the first step of AES encryption I see that we XOR the key with the plaintext block. Why is the actual key involved at all, why not just use the round keys derived from the key schedule?
Consider the following version of padded RSA encryption, where encryption of $m$ is done by setting $m′ = (0^k~||~r~||~00000000~||~m)$ for a random $r$ (of length 8 btyes = 64 bits) and then computing the ciphertext $c = (m′)^e$ (mod $N$). For concreteness, further assume that $N$ is a 1024-bit RSA modulus, and that th...
I want to encrypt a small piece of data that is less that 16 bytes in size (think SSN), and I'll be using a 256bit encryption key. The typical suggestion is to never use ECB, but if there is just a single block being encrypted, is it a concern? The reason I want to use ECB is because I want the encrypted value of the ...
I would like to be able to encrypt the output of RSA with RSA again without having the output grow in size over time. In other words, I have some data $D_0$ which I want to encrypt with RSA: $D_1 = \mathrm{RSAencrypt}_{K_1}(D_0)$. Then, I would like to be able to encrypt $D_1$: $D_2 = \mathrm{RSAencrypt}_{K_2}(D_1)$, a...
CipherCloud claims to support , among other things, searchable encryption. A bunch of speculation seems to suggest they did this via some breathtakingly incompetent means( unfortunately such speculation "appears" to be copyrighted) Regardless of their actual methodology, if we assume their encrypted data is searchable...
Shannon's paper states: A system is pure if all keys are equally likely and if for any three transformations, $T_i$, $T_j$, $T_k$ in the set, the product $T_iT_j^{-1}T_k$ is also a transformation in the set. But this is exactly the construction of Triple-DES! So, using this terminology, it is not a pure system, s...
When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$. I believe this would be the correct solution (correct me if I'm wrong): Each party computes $x_i + y_i = z_i$ Each party shares $z_i$ with the other 2 parties Each party uses Lagrange basis polynomials to ...
Given a ciphertext $y$, describe how to choose a ciphertext $\hat{y} \neq y$, such that knowledge of the plaintext $\hat{x}=d_K(\hat{y})$ allows $x=d_k(y)$ to be computed. So I use the fact that the decryption function is multiplicative: $d_K(y_1)d_K(y_2)= d_K(y_1y_2)$. Thus we have $d_k(y\hat{y})=x\hat{x}$. Now if $y\...
I've been toying with some encryption scenarios recently. One of the hard ones I came across is a multi-party system. So we have Bob -- The person who sends the message (and knows it's recipients) Jim -- The person who supervises who is capable of decrypting the message(but can not decrypt the message himself) Alice ...
Another approach taken by researchers for carrying out computations over encrypted data is Instance Hiding. In brief, If a user wants to outsource the computation of a function for a particular input x (instance). She transforms the input x to an encrypted input y (thus hides it) in such a way that the server cannot in...
Suppose that the only public key cryptography schemes that we knew were Diffie Hellman, RSA and ElGamal. How much would this set civilization back? Are there important applications of elliptic curve cryptography [specifically] without viable substitutes? [Edit: I came across this question which gives some information, ...
I have been working on a project implementing LT codes with Homomorphic hashing (inspired from http://blog.notdot.net/2012/08/Damn-Cool-Algorithms-Homomorphic-Hashing and http://blog.notdot.net/2012/01/Damn-Cool-Algorithms-Fountain-Codes). Here's what I have understood from those links. Suppose the message to be sent a...
For example, in my situation I know hash(20) = 486e9638177faf1f34e49910491b77af. I also know the hashes for all values from 0 to 20. Is it possible to work out the algorithm used to hash these values?
Is it a weakness to use a single shared secret for protecting messages using a Encrypt-then-MAC scheme? Assuming a system is using AES-256-CBC and a SHA1-HMAC and the same secret key for both operations. Upon intercepting one of these messages and attacker could brute force this secret key by trying to solve the HMA...
Has anyone checked if using haveged, a Linux daemon which uses the HAVEGE algorithm, changes the non-deterministic properties of the random data from /dev/random in any negative ways?
This is a follow up to Is It Possible To Reconstruct a Cryptographic Hash's Key I am using a SHA-256 HMAC function on a single-word input: sha256hmac(privatekey,word) = output. The private key length is 128 bits, it does not change. The "word" is literally one short word. Assuming an attacker knows "word" and "output" ...
I am designing a simple and secure stream communication protocol. My idea was to build each message sent to the wire as: (message size || clear text || UHASH(message size || clear text)) $\oplus$ unique stream cipher output where UHASH is the main function from UMAC (see question Using UMAC with stream cypher), || is c...
It's more a theoretical question of how would you approach it. All you know about the ciphertext it's was generated with a historical cipher. The ciphertext appears to be random, BUT it's divided into sets of six letters. By historical ciphers I mean: mono (Ceasar), polyalphabetic (Vigenere), homophonic or polygraphic ...
For a cryptographic hash function and input values of shorter length than the hash function output, it's pretty obvious that there should be as few collisions as possible. But are there guaranteed to be none? In other words, for a cryptographic hash function $H: x\to y, x \in \mathbb{N}, y \in [0,y_{max}]$, are there a...
Assume there is a crypto algorithm that deals with matrices to encrypt and decrypt. Regardless of the specification of such algorithm, what if the algorithm assumes that two parties can securely agree on a matrix and use it along with its inverse to encrypt and decrypt? What I am trying to understand, is that, such thi...
Problem Overview I want to securely store log files so the contents are secret, and they can't be modified without detection. The files will be encrypted using authenticated encryption (AES in GCM mode), with a random IV and symmetric key for each file. The symmetric key will be encrypted using the public part of an RS...
Is it possible to find out which public key was used to generate the message? Scenario is like this : I got data which is encrypted with a public key. Now a "bad guy" hast the encrypted data, and knows the decrypted content and wants to know who was the receiver of the data. The "bad guy" has all possible public keys w...
'Hybrid' encryption, where we combine symmetric encryption with public-key cryptography, is pretty 'tried and tested'. To summarise, we generate a symmetric key and encrypt it using RSA. We would encrypt our data using the symmetric, and prefix it with the IV and encrypted key. You therefore need the private key from t...
I was wondering what "securely realizes" means. I see this in some cryptographic papers but I don't know what it means for a protocol to "securely realize" a function $F$. Is it just a fancy way of saying "uses" or does it mean something else?
I have thought up a method for generating random numbers between a client and a server which I hope is fair: The client and server decide on a range in advance, $0$ trough $n-1$. The server generates a $256$ bit random number $m$ (in the range $0$ to $\operatorname{floor}(\frac{2^{256} }{ n}) · n$) and hashes it with ...
I read that to break repeating-key xor you can do the following: try a keysize $n$ and compute the hamming distance between the first $n$ bits of the encrypted string and the bits $n+1$ to $2n$ of the encrypted string and normalize by keysize. The true keysize probably minimizes this. Why? It also suggests to average a...
I'm looking for feedback on whether or not this is the proper way to approach password verification without transmitting the actual password. Are there any problems with this scheme. We are working on a cloud based encrypted file system and have implemented the following steps to verify that the entered password is the...
We are currently developing a little AES implementation in a crypto-course at university. As far as I know, AES uses a 128 bit block length, so all data that will be encrypted gets split up into blocks of 128 bits (16 bytes) into a 2d-array (or 1d in implementation) with 4 × 4 fields. I was wondering and didn't find ou...
I'm pretty sure there are famous algorithms for my problem, but I don't have enough knowledge in this field, so I need your lights. Here si the problem : Alice sends key X to Bob. Bob has an function that given the key X and the time, generates a key Y every 30 seconds, which is valid for 30 seconds. If Bob send the m...
If I correctly understand the concept of a "brain wallet" in BitCoin, you start with a passphrase, generate the hash of the passphrase, then somehow derive a public / private key from that to use as your BitCoin identifier. This conflicts with what I understand about key pairs... namely that they are special... not eve...
Let's say I want to create private archives for the long term (e.g. more than 30 ). The archives' sizes could be anywhere from 1 GB to 30 GB. As far as I understand I could go down two ways: The first would be for example using plain AES-256 encryption in CTR mode with a random key stored on paper. The second, more su...
Given nothing more than some integer $m =$ OAEP($M$), is it possible to recover the original plaintext $M$? In other words, without being given the hash functions or the random string used for encoding, or even the length of it. EDIT: This is being used in tandem with RSA, but I don't know the hash functions that OAEP ...
I understand that when you want to encrypt and sign data with RSA the generally recommended approach is sign-then-encrypt. However, I have encrypted data that I need to sign, to prove the author of the encrypted data. Encrypt wth recipient's public key Sign with author's private key Concatenate cipher text with signat...
If an adversary knows my public key and guesses what was my plaintext, can he test for it somehow? The most obvious way is encrypting the guessed plaintext with my public key and the same parameters that he can probably discover from the ciphertext, to see if the result is the same.
I am just reading the "soundness" definition for proofs of knowledge by Bellare / Goldreich. A proof of knowledge is a proof between a prover $P$ and a verifier $V$. $P$ convinces $V$ of his knowledge of a secret value. The idea is to define a knowledge extractor $K$, which can calculate the secret. They write There e...
How can I derive formulas for adding 2 points and multiplication by a scalar in Jacobian coordinates $(x,y) = (\frac{X}{Z^2},\frac{Y}{Z^3})$ over an elliptic curve?
Is there some standard protocol for mutual authentication of two parties when there is possibility to use public key cryptography? The problem is that two parties can use public key cryptography but public keys are not embedded within any kind of certificates. Is there a way to avoid MITM attacks? Simple use of public ...
Given we are using AES counter mode, suppose we randomly generate several keys, all of them are using same IV (say, zeros). Does this lead to any security issue? I know that in CTR mode, same key-iv pairs would lead to two-time-pad. But the above construction will not have the same keys. In application: Let's say Alice...
As I describe in my previous question I am trying to decide if it's worth it for me to use the Offline Private Key Protocol in creating some long term private archives, instead of just going with a simple symmetric encryption like AES-256. The answer to that question pointed out that using RSA to encrypt the symmetric ...
For primes p and q used to create a keypair, I understand that the following operation is used to create a signature: $M^d (\bmod\ N)$ where d and N have their usual meanings and M is the message. In this case, however you need to possess the public key in order to verify the signature S as follows :- $S^e (\bmod\ N)$ ...
After reading these two resources I am wondering am I getting all the differences between Scrypt and PBKDF2. As far as I understood, the similarity is: both are password-based key derivation functions. The difference is: Scrypt is more resource demanding. Am I missing something?
Is there a construction of an order preserving hash function that keeps the preimage property of a crypto hash function? By order preserving hash function (OPHF) i mean for $x<y$ then $OPHF(x) < OPHF(y)$
I will be making (in the near future) an app that will contain some pretty heavy crypto. As it is possible that my app will be ported to different devices (initially it will be iOs only, but Mac, Android & maybe even Windows ports will eventually exist). The question is how to make the crypto library as portable as pos...
I'm looking for a toy hash function, where the idea is to have high school students break (i.e. find a collision) a hash function by hand, in order to teach them how one way functions and hashing works. Do you happen to know some function like that? As for how hard I want it to be to breakable: Ideally a "sizeable" fun...
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 any $Gen$...
In my lecture, the lecturer said: Let $K$ be the key generation algorithm. Given a security parameter represented in unary, $1^k$, $K(1^k)$ will output a keypair $(pk; sk)$, known as the public key and the private (or secret) key, respectively. My question is: When I want to implement the cryptosystem, how should I...
I am read this paragraph and I have a doubt. "An adversary to PKC $\Pi$ is given by two probabilistic polynomial time algorithms, $A = (A1; A2)$. In the first stage, the "find" stage, the adversary analyzes the public key and tries to determine which plaintexts, when encrypted, are vulnerable to attack. This is ...
I'm referring to page 383 of J. Katz and Y. Lindell's Introduction to Modern Cryptography. The book presents a padded RSA: ${\bf Key Generation:}$ same as Textbook RSA (given security parameter $1^n$, generate public key ($N,e$), secret key ($N,d$), such that $N = pq, ed \equiv 1 \mod{(p-1)(q-1)}$) ${\bf Encryption:...
In an answer to a previous question it was suggested that one way to protect your asymmetrically encrypted AES-256 keys, from say a solution to prime factorization, would be to chain asymmetric algorithms. Having read about the meet-in-the-middle attacks here and there I am a bit worried that if I chain, say RSA with E...
what should I do if my original message is greater than 64 bits? what is the process of padding in MD5? As described in Internet Security: Cryptographic Principles, Algorithms and Protocols, page 138, the second step in MD5 is to append the length of the message: Can someone help me understand exactly what happens whe...
Ok, I hope this question makes some sense because I am not so sure how to word it any differently… Imagine the following situation: There are 10 defined colors (blue, orange, yellow etc.) There are 2 Persons and each of them has 1 favorite, secrete color The 2 persons don't know each other's favorite color, however, ...
I'm building a basic HSM out of an Arduino, and am using the following scheme to store data: Master symmetric key $k_m$ stored in firmware (secure bit set to prevent trivial extraction). Secondary symmetric keys $k_s$ stored as plaintext in web application database, one per user. HSM record key $k_r$ generated by xor'...
$H(s,r)=d$ is a function that hashes the secret string $s$ with a salt $r$, and returns a digest $d$. $r$ may be arbitrarily chosen and each $r$ returns a different $d$. For any $d$, $r$ is known from a function $R(d)=r$. Both $H$ and $R$ are not reversible, i.e. there isn't a neither a reverse function $H'(d,r)=s$ n...
I want study more about cryptography reading papers, but I have a problems to understand few concepts: security notions, random oracle model, IND-CCA, ... etc. I began study this concepts by internet: wikipedia, sites etc, but I like have a didactic book to learn this concepts. Please anybody will be able to recommend ...
I want to do a one-sided integer commitment scheme. I.e. the whole process must be non-interactive where I at one point first publicly reveal some data and then at a later time reveal the committed integer which then can be verified. In the pedersen commitment scheme we have six pieces of data $p$, $c$, $g$, $h$, $x$, ...
Encrypt a single file, chunk-by-chunk, each chunk using different key. I am a security newbie (only took 2 security courses before) But currently I am using this encryption method for my Android application, which perform client-side encryption and upload each encrypted chunk into different cloud storage (Dropbox, Box,...
How much will the security of one-time pad decrease if I use one digit from 0-9 instead of 1-26? for example plaintext = "blue" and key = "5 9 4 6": b l u e - plaintext 02 12 21 05 - plaintext in numeric form 5 9 4 6 - key 07 21 25 11 - ciphertext in numeric form g u y k - ciphertext so blue + 59...
CBC-MAC, with fixed length message. Is it safe to return all ciphered blocks instead of the last? My intuition says it is less secure, since is gives an attacker more information. But how could one attack this scheme?
I am wondering what length the padding should be when encrypting or signing with RSA. Does it matter what length the padding is, and if so — what length should it be? Another point: Should it be random?
can we reuse same ECC key on TLS for long terms or it must be used just once? (i mean can we use ECC like RSA?) is there patent free ECC implementation ?
I've read almost everywhere that AES-256 can be used for Top Secret material (in the US). Is it really used or is it some kind of decoy to hide the more advanced algorithm they might use ?
What is the best way to generate two independent symmetric keys from one user-entered password or passphrase? Would using both scrypt and pbkdf2 achieve this?
I want solve the next exercise. The author defined the experiment for the cryptosystem $\Pi$, the adversary $A$ and the security parameter $n$ as follows $\mathsf{PRIV_{EAV}}(\Pi,A,n)$ The adversary $A$ get the input $1^n$ and choose two messages $m^{(0)}$, $m^{(1)} \in M$ with same length; One key $k \in K$ is genera...
Is there any difference except speed and key and block size from user's point of view? Or does AES have something that ideal block cipher doesn't have?
Some ciphers are talked about at “Is there a secure cryptosystem that can be performed mentally?”, but (at the time of writing) I don't see an answer. Are they strong enough, or are non-computer ciphers more or less just a toy and one should abandon using them for practical purposes?
I am trying to implement Shamir's secret sharing in C++. I have got the generation of shares working. However, I am very confused with the reconstruction of shares. I get the part on how three users can reconstruct the secret. But what if there are more than 3 users needed to reconstruct the secret? How do I implement ...
I want to store a password securely on a storage (suppose in a usual unencrypted file). I use this password as AES key to encrypt itself (using AES-ECB) & then store it on the media (the password length is at most 16 bytes). When user wants to confirm it's identity, I decrypt this saved encrypted content with user inpu...
SRP seems to be a very good password authentication protocol, compared to any other things used now. So why is there no popular implementations, or even no working secure implementations? I tried to set up TLS-SRP protocol, but it haven't worked for me. Haaalp! Someone?
Suppose you randomly generate large primes p and q as in RSA, and then tell me N=pq but not p or q. Then, you would like to actually let me factor N, except you should tell me as few bits of information as possible. Say p and q are 4096 bits, then how many bits do you need to tell me in order for me to factor N in feas...
I am trying to calculate an $x$, such that $t = g^x \pmod p$ in order to crack a weak ElGamal encryption for university. I found GDlog, but I cant figure out how I can use the input to calculate my $x$. Here is what we got (from gdlogs example code): p:1000000000000000000000000000057 //prime number, modulus q:2902400...