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I only use one gpg key, which I use with pass, which currently holds a ton of password stuff. I also use that key to sign my github commits and a ton of other stuff. I leaked my key by posting my private key, thinking it was my public key on my github profile (it's been up for a couple of days now, and I just realized ...
MPC protocols have a harder time handling division (truncation) than multiplication. The case I am considering is when the divisor is a public value. Dividing it may lead to a wrong result due to wrapping around the ring, or we need to pay more cost to get a faithful result. But if the divisor is public, parties can co...
Traditionally, I think that implementing the CRS (common reference string) model in the real world is usually through a trusted third party or running a distributed protocol. Are there specific papers on this that I can refer to? Thanks a lot!
A pseudorandom correlation generator for bilinear correlation (namely, $x_0 \otimes x_1 = z_0 + z_1$, where party $\sigma$ gets $x_\sigma, z_\sigma$) over some field $F$ works roughly as follows (based on Figure 14 of https://eprint.iacr.org/2022/1035): Gen: Pick two random sparse vectors of weight $t$ $e_0, e_1 \gets...
new member here. I am taking a course in computer security, and we just got introduced in Cryptography and especially in RSA Algorithm. Although i got the 'basic idea' behind the RSA algorithm and the prime numbers needed for the keys, we have an assignment. Roughly the content of the exercise, is this : Suppose an RSA...
The question is what is an appropriate public/private key length in order to encrypt a 256-bit or 512-bit AES key without wasting bytes, and whether long public/private keys provide meaningful increase in security simply from being longer. I'm encrypting a 256-bit AES key using a public key from a 2048-bit private key....
I've been recently thinking about building a c++ poker game that would let players to play over sockets in a peer to peer network. However I do not know how security would be ensured. I was thinking that whenever a particular player has a turn, they alter the game state and then they broadcast this game state to the ne...
If you were designing: An open source client that offered E2E encryption for e.g. folder sharing between users Each user had public keys for signing (and separate public keys for encryption of symmetric keys etc, but this is not what the question is about). The service is extra cautious by default (wanting to be extra...
As I know a very common hash code has 256 bits. From a message, it outputs a hash code that's 256 bits. That hash code should be unique to that message. That message can be something like email. But a message can be very long, far longer than 256 bits. Theoretically there can be 2^256 different hash codes, and that's i...
I am trying to understand the implication of the Borel-Cantelli Lemma to the random oracle model. I think understanding a special case, say, a random oracle is one-way with probability 1, would be helpful. The statement (see, e.g., page 19 of Arkady Yerukhimovich's thesis) as far as I understand in words goes like "if ...
I'm creating an application where I'm going to use Argon2, I'm going to have a password, and I'm going to use as salt: email+name+date of birth, you must think that my salt is silly because name and date of birth can change, which would change the result, well this is not the case with my application, I should and will...
Following ciphersuites found to be weak in Qualys(https://www.ssllabs.com/ssltest/analyze.html) tool: TLS_ECDHE_RSA_WITH_AES_128_CBC_SHA256 (0xc027) ECDH x25519 (eq. 3072 bits RSA) TLS_ECDHE_RSA_WITH_AES_256_CBC_SHA384 (0xc028) ECDH x25519 (eq. 3072 bits RSA) TLS_DHE_RSA_WITH_AES_128_CBC_SHA256 (0x67) DH 4...
I know that both algorithms are similar to the Diffie-Hellman key exchange and are used for exchanging secret keys in a group but I still cannot figure out the key differences between both algorithms. Is the difference only in the number of rounds that are required to exchange the keys? I would appreciate an in-depth e...
As Bleichenbacher states, a wrong implementation of the parsing function of the padding could lead to a signature forgery attack when using a low exponent. In the provided example he assumes the attacker has the freedom to put chosen bytes in the "garbage" section at the end of the message, in order to create a perfect...
I will be using a tRNG to generate EC keypairs on a Secure Integrated Controller. I need to demonstrate I, the issuer, can not know the private key without colluding with the user to obtain it, even if the tRNG is weak. I also don't want to reveal the private key to the user, only the public key. I'm thinking a scheme ...
I don't understand why I need a salt for Argon2 if Argon2 is only needed as a KDF for a password which is then called AES. At the end neither the password nor a password hash is stored. Only the data which was encrypted with the KDF key. It is logical that when storing passwords in databases a salt is needed to prevent...
I am trying to implement an electronic voting scheme which uses the exponential version of elgamal cryptosystem, voters encrypt their votes for each candidate and send them all to the ballot box. Now each ballot contains the encryption of either 0 or 1 for each candidate in a determined order, vote's validity gets chec...
[Moderator note: this question now lives there] So, I'm preparing a talk about the well known fact that humans are bad at the task of generating uniformly random sequences of numbers when asked to do so, which is a huge flaw for simple cryptographic systems. I would like to spice the talk a bit by present some real cas...
Xorshift family pseudo-random number generators have a variety of different internal state sizes. Let's take one of this family called xorshift1024*. My question is: Having xorshift1024* a internal state of 1024-bits, can I generate a block shorter than 1024-bits without having to compute the entire 1024-bits output be...
Want to get 32 bits from 0x8000 address as 8 bytes (perm box) MEM_EXT:00008000 db 54h MEM_EXT:00008001 db 53h, 57h, 20h MEM_EXT:00008004 dd 322E3256h, 31332030h, 30303330h, 31313320h, 43432036h MEM_EXT:00008004 dd 2F363535h, 20425345h, 865808FAh, 865808FAh...
Is there a known example of a deterministic algorithm that given an n-bit input returns 2n-bit output, and where a random output can't be efficiently distinguished from a random 2n bit string?
I know that there are papers for both theoretic and practical zk snark computation. And most of them could support general computations. i.e: support multiplication and addition But what I am curious about is that are there papers/constructions that optimize the exponentiation computation, not just having a^n compute...
I am looking to get P-box and S-box from firmware Decided to search the firmware for Pbox - 8 nibbles from 0-7 i.e pbox = [2, 0, 6, 5, 7, 4, 3, 1] Found it :) And for S-Box 16 bytes from 0-15 (based on my research on S-box) i.e sbox = [5, 11, 7, 12, 4, 8, 0, 3, 13, 9, 6, 1, 2, 14, 10, 15] However cannot find it in fi...
Background Bob's goal: Receive data E = E(D) (encryption of D) from Alice that he knows for sure is encrypted and that he can't possibly decrypt (without brute force). This gives his data backup company peace of mind - no need to worry about what sorts of data he stores (copyright issues, etc.). When Bob sends E back t...
I hope this question is not too basic. I'm currently trying to implement compact proofs of retrievability that are publicly verifiable by BLS scheme as described in this paper Compact Proofs of Retrievability in GO. I already implemented it with RSA and now I want to do the same with the BLS Scheme as described in sect...
I am currently writing a seminar paper on Kyber and other lattice-based methods. I was so excited about the lattice-based methods that I also currently searched quantum algorithms to solve the methods. In the process, I came across this paper: https://www.mdpi.com/1099-4300/24/10/1428/pdf, called "Using Variational Qua...
What is the best progress (i.e. most bits) in crafting messages with a chosen hash image for modern hash functions? Blockchain networks with proof of work are basically brute force machines for pre-image attack on keccak with a target image of 0x000.000. So I was looking for some idea of what the "best hash" ever found...
I asked OpenSSL to generate a dummy Ed25519 private key for me and got this output: https://lapo.it/asn1js/#MC4CAQAwBQYDK2VwBCIEIJCO9eKZEUOmL9CGfecuKqvYU_hLTAFXwl0Ipd8xNXbP It decodes to the following: SEQUENCE (3 elem) INTEGER 0 SEQUENCE (1 elem) OBJECT IDENTIFIER 1.3.101.112 curveEd25519 (EdDSA 25519 signatur...
When the last n bytes of the plaintext are themselves suitably random, but predictably repeat m times in the same message - how bad is that? I'm convinced it is detrimental, but I am uncertain how detrimental exactly. Edit: assume a Padding Oracle to be available. NB: I'm not asking about the same overall plaintext sen...
When i list down the curves using openssl ecpram -list_curves where in which I didn't see any curve named FRP256v1. Does openssl actually supports FRP256v1? If so can you please let me know the version in which the support for this curve exists? The openssl version where in which I checked this is OpenSSL 1.1.1 11 Sep...
I am currently developing the back end of a website for one my projects and needed to store passwords. I knew that I needed to store passwords with salt, and my initial approach was to just generate the salt and append it to the password. However, to check that I wasn't being stupid I looked it up and saw a multitude ...
What is the best known attack on the stream cipher Trivium? And is there is any good reason to not use it? By googling the good key words, I've found this paper, but I'm not enough expert to judge the relevancy of this paper.
I've seen (on Wikipedia) in the more recent version of TLS, the Counter-mode was not used. But the Galois-Counter-mode was used? What is the advantage to use the GCM instead of using the Counter-mode?
This is with reference to Eddie Woo's video on RSA. He uses the prime numbers '2' and '7' to make the product, n=14. He chooses the public key to be '5', the only possibility. However, many numbers meet the criteria to be the private key, where (5 * private key mod 14) = 1. To name a few, the numbers include 5,11,17. E...
I wish to encrypt an image using Logistic map. A Logistic map can be specified with the Equation: $$x_{n+1} = r\,x_n (1-x_n).$$ Now, according to the Kerckhoff principle, the entire system's security is dependent on the key. Perfect chaos can be achieved with a fixed control parameter ($r$) and initial condition ($x_0$...
I wondered whether my understanding of entropy is correct, that a 256-bit counter that starts at 0 and counts to 2^256 - 1 by a +1 increment has a 256-bit entropy. I am asking this because I felt it awkward that for RNGs, developers often only specify an entropy. So is it correct that a non-repeating 256-bit counter ha...
I want to accredit members so they can pseudonymously give feedback while still being provably part of a group, without a way to give extra accreditations. Suppose a group of 100 members (I decide and make public who these members are) want to bit by bit create 100 accounts such that nobody knows which member created w...
Several years ago, there was an unenforced constraint on verification in the cirmcomlib library : a tool for building projects using ZsNarks. The error allowed to forge cryptographic nullifiers/proofs without having a prior commitment. Tornado Cash, using Groth16 was the most well‑known affected case : the protocol had...
I have been asked to make a HMAC-SHA256 password digest from: a password some salt, and an 80-bit secret key. I've been advised that I should be using a key of 256 bits or more for HMAC-256. The key I have is only 80 bits. Is there any value in using sha256(key80bit) as the key for HMAC-SHA256, as it will not increas...
I'm implementing impossible differential cryptanalysis on 3.5 round IDEA using the methods in "Miss in the middle attack on IDEA and Khufu" paper. In the first step, I need to provide $2^{32}$ pairs that are identical in $X_2$ and $X_4$ and have all the possibilities in $X_1$ and $X_3$ to start the cryptanalysis. So I'...
Why are credit cards using 3DES instead of AES? As far I understood, even DES3 is less secure than AES. Why it is still used? I searched already in the internet and forum to check out if it is meanwhile AES (and the information from my lecture may be just old) but I didn't find any clue for that.
When we consider a group generation algorithm $\mathcal{G}$ (taken from Katz and Lindell's Introduction to Modern Cryptography), that takes as input a security parameter $1^n$ and outputs $(\mathbb{Z}_n, n, g)$, where $\mathbb{Z}_n$ is an additive group, can we say that the DDH, CDH, and discrete logarithm assumptions ...
The original description of the MD5 algorithm initializes the values of A, B, C, and D to the following: word A: 01 23 45 67 word B: 89 ab cd ef word C: fe dc ba 98 word D: 76 54 32 10 How were the values determined and does it matter how they were chosen?
I'm trying to formalize the following protocol in $\mathsf{ProVerif}$, where $m$, $p$ are messages, $j$, $k$, $h$ are private keys, and $\{m\}_k$ is the ciphertext obtained by encrypting $m$ with $k$. Furthermore, $f$ and $g$ are functions whose result does not reveal any information about any of the two arguments. I a...
I am curious what is an attack that the RSA Key Exchange algorithm is vulnerable to that Diffie Hellman Key Exchange is not vulnerable to? I know Diffie Hellman is prone to Man in the Middle attacks but when performing key exchange with RSA, is it also susceptible to some attacks that Diffie Hellman is not to?
I'm writing a school paper about Blowfish encryption, and couldn't seem to find out if the size of the subkey array for Blowfish changes based on the length of the key. I would assume that it doesn't effect the size of the subkey array but I'm relatively new to Blowfish encryption.
I've got a scheme where I XOR a secret key value with a public (but random) value, XOR together all the bits of the result, and publish that bit (0 or 1), which is the parity of the result of the XOR. My goal is for this published bit to be hard to predict, for a given public value, before it is published. I'm certain ...
I was reading the Wikipedia page for scrypt because I wanted to learn more about it and I came across their pseudocode for the algorithm. What confused me was the following line: I don't understand why having (what I assume to be) an output length of 32 bytes would make it in any way associated with SHA-256. Yes, they...
Can we devise an attack on AES or DES (ECB mode) if we know just the distribution for the plaintext? For example, it is a English plain text -- we know what that would look like and the relative frequencies of letters, bigrams, and trigrams? Has anyone come across such type of attacks, it is a advanced version of known...
The Wikipedia page for BLS digital signature describes a scheme with only two groups, $G$ and $G_T$, and a bilinear pairing $e: G \times G \rightarrow G_T$. To the best of my understanding, in such a scheme both public keys and signatures would belong to the same group $G$, signature verification being performed by com...
TL;DR: My simple ChaCha-based sponge PRNG is getting "unusual" evaluation from PractRand test battery pretty reliably, sometimes even within the first GB; I'm trying understand why. I was in need of a fast, non-cryptographic PRNG, preferably one without a bloated state, or one that would use a portion of its internal s...
Are there any automated security protocol verification tools that model algebraic operations; specifically addition. I am familiar with AVISPA and Verifpal, and they are both great and user-friendly tools, but they do not support addition operation. Please help
Here is the fixed script # Generator point coordinates x=55066263022277343669578718895168534326250603453777594175500187360389116729240 y=32670510020758816978083085130507043184471273380659243275938904335757337482424 # Order n=115792089237316195423570985008687907853269984665640564039457584007908834671663 # from the curve...
IBM (now HCL) Domino has since way back a complete procedure to issue X509 client certificate as a login option to a webserver. Back in 2010-ish it worked fine in both Firefox and Internet Explorer. The handling has 4 steps Acceptance of Root certificate, CA (usually self-signed from Domino) Request client certificate...
I know about the existential forgery attack on RSA where a forgery is possible given two valid message and signature pairs but I am wondering how can a forgery be done on RSA with just the knowledge of the public key (e and n) without the knowledge of another message/signature pair given that the signatures are not pad...
I'm working on a project with two computation "phases". In the first phase, I would like to homomorphically compute operations on my ciphertexts with a plaintext modulus of 2. But for my second phase, I would like to use a different plaintext modulus say 12799. Without decrypting and reencrypting my results between pha...
I have been puzzled by the following for a long time. In the (very well know in the field) paper: Improved Non-Interactive Zero Knowledge with Applications to Post-Quantum Signatures , the authors introduce the so-called cut and choose technique to produce zk proofs. In particular, they show how to prove that $y=f(x)$ ...
Are their any attacks on AES (any mode) in which before the attack is mounted, the adversary is aware that the input distribution is non-uniform? Most of the work assume that the plaintext is uniformly distributed. This is with reference to the following paper- https://eprint.iacr.org/2019/491.pdf
The problem I have is next: There's the centralized DataBase app which has its own private key and sends its public key to its customers. Each customer has its own private key and should be able to use the combination of his own key and DB app's public key to encrypt its own data. The encrypted data will be visible/av...
I have noticed that points on a NIST curve (secp256, secp384, etc.) or some other elliptic curves used in cryptography, when represented as 04 | x coordinate | y coordinate in hexadecimal, the coordinates appear to have a fixed length. Is this something that is proved somewhere ? As far as the math goes, I do not see a...
Choosing a proper nonce is a vital part of every symmetric-key encrypted communication, and it is mandatory that every encrypted message has a unique nonce. It can be shown that using a nonce twice with the same key has such catastrophic effects on the system. So in every protocol that uses AES-GCM or other AEAD algori...
Is 7-Zip really a good encryption tool? I wonder what kind of encryption is used in 7-zip. I see most people using 7-Zip. Just curious about what extent it is safe.
I'm searching good libraries to manipulate lattice tools to do cryptography. I'm mainly interested by C/C++. But I'm also interested if it is in python.
How Schnorr signature security can be proved for signature forgery, replacement, and Replay attacks?
I'm looking at the following text: Why does CKKS decryption have an approximate correctness requiring that $\|u + e\| < {q / 2}$? I mean if $\|u + e\| \ge {q / 2}$, how can I prove the CKKS decryption doesn't have approximate correctness?
In section 4.3.2 of this paper describing the BabyJubJub curve, an algorithm for computing the scalar multiple $[k]P$ is given, where $k$ is in arbitrarily large integer and $P$ is a point whose order is $251$ to $254$ bits on the BabyJubJub curve. In this algorithm, $k$ is 'split' into chunks of $248$ bits and the alg...
ElGamal-based BBS proxy re-encryption is well known, but it works on a variant of ElGamal like ($mg^r$,$g^{xr})$ not standard ElGamal ($g^r$,$mg^{xr}$). After reading the original paper, I found the authors mentioned that the proxy scheme can be extended to work with standard EIGamal encryption. But unfortunately they ...
A KDF in Counter Mode (e.g., see NIST SP 800-108r1, Section 4.1, similar to HKDF) produces the output as what AES-CTR would do if one replaces AES with SHA2 (or, to be exact, with HMAC). However, NIST, Section 6.3 does not recommend using the derived keying material as a key stream. As far as I understand, they mean th...
The wikipedia article on the Advanced Encryption Standard claims an attack against AES-128 with complexity $2^{126.1}$. The NIST call for proposals for post-quantum cryptography (table on page 18) estimates $2^{143}$ classical gates for key-search attack against AES-128. What does the number in the wikipedia article m...
I am trying to get into Universal Composable Security, but before diving deeper I would like to confirm my intuition of the framework. https://eprint.iacr.org/2000/067.pdf A protocol $\pi$ securely evaluates a function $\mathcal{f}$ if for any adversary $\mathcal{A}$ there exists an "ideal adversary" $\mathcal{S}$ suc...
How do I calculate the soundness error of a sigma protocol, such as Schnorr's interactive protocol for knowledge of a discrete logarithm?
In this paper by Alperin-Sheriff and Peikert from 2014, the authors state To date, bootstrapping remains the only known way of obtaining fully homomorphic encryption for arbitrary unbounded computations. Is this still correct today or are there new schemes that don't require bootstrapping for the same effect? Are the...
Purpose: I'd like to shuffle a file system's blocks without loosing space so I thought if I formatted the disk to have exactly 2^32=4bn sectors, then a secure cipher with 32 bit wide data blocks could map all sectors to new ones without wasting place, like a hash map would do due to its collision chances.
Blowfish encryption is made as follows: 1 - XOR the round key with half of the plaintext. 2 - Split the 32-bits word in 4 bytes and insert each one in the S-Boxes. 3 - Sum the result of byte #1 with #2 and XOR in the result of byte #3 4 - Sum the above result with result of byte #4. 5 - XOR the result of the above oper...
I started studying again recently, I forgot plenty of stuff. But there are 2 areas that I am really struggling. The procedures to prove and demonstrate theorems. The basic math necessary for cryptography. Do you guys have any books and references that are easy to learn about those two items? Thank you!!
Suppose we have two plaintexts $m_1$ and $m_2$ such a way that $|m_1| = |m_2| = 128 $ and these two plaintexts are different just in one bit. Now suppose we know the value of $c_1 = AES_{k}(m_1)$($|k| =256$) . What is the best complexity of guessing difference $c_1 \oplus c_2 = ?$ with probability at least $\frac{1}{2...
I have developed a project based on Raspberry Pi that communicates through Bluetooth with Android application, My idea is to enhance its privacy through encryption. So, I've tried chaotic encryption. But I've observed a higher lattency while encrypting & Mainly I was dealing with images..It is adding up a lot of noise ...
The AES algorithm uses the irreducible polynomial. Consider x^8+x^4+x^3+x+1 for multiplying with a MDS matrix for encryption and decryption. Am I allowed to change this polynomial with another one? If so, then I need to redesign the MDS matrix? Does this effect security standards?
I'm working on a protocol and am looking for a way to fingerprint a set of elements. All elements are evenly distributed across a finite field that is integers modulus $2^{256}$. Assume I have a set of elements $[v_0, v_1, v_2, v_3]$, and a strong random value $R$ (also in the field). I construct a hash like this $H = ...
Suppose we have a plaintext $m$ and $|m| = 128$. Now suppose we know $l$ bit of the output $AES_k(m) = c$. What is the best complexity of guessing the rest $128-l$ bits of output with probability at least $\frac{1}{2}$. Note that we don't know the value of $k$
I'm interested on the polynomial used in GCM-mode : $X^{128}+X^7+X^2+X+1$ This polynomial is Primitive (in $\mathbb{F}_2$). What is the interest of choosing a primitive polynomial and not a simple irreducible polynomial? Is it a coincidence?
How do new cache designs aid in defending against cache-based side-channel attacks? While conducting a side-channel attack, we have the T-table/S-virtual box's address. Normally, address mapping is handled by the operating system. An adversary can always determine the virtual address. How will a new cache design help? ...
Can we encrypt data with two public keys and the encrypted data only needs one private key to decrypt once encrypted?
In (lattice-based) cryptography, the quotient ring $\mathbb{Z}[X]/(X^n+1)$ where $n = 2^e$ is a power of 2 is used in various cryptographic schemes (e.g., CRYSTALS-Kyber). It is my understanding that this is a common choice because we can efficiently compute products in this ring using the Number Theoretic Transform (N...
This is an example of a bitlocker recovery key; 820042-335825-646573-481530-265253-688132-339900-822810 İs that key actually strong? It does not have any letters, it uses only numbers, so is it OK?
I've been implementing RSA as a learning exercise and am at a point now where I'd like to try serializing my key to a file using some standard format. I've implemented it without using the Chinese Remainder Theorem, so my private key is composed only of my modulus $n=pq$ and my modular inverse exponent $d$. I've seen t...
Why is it that most implementations define an sha256_init, sha256_update, and sha256_final function that each operates on a SHA256_CTX object? The specification only mentions returning an almost unique hash for any given string of bits of any given length. What is the reason to have these 3 functions instead of just a...
I wonder if there is any practical attack on MD5(key || fixed-length-message).
IKEv2 RFC7296 Section 2.16, provides overview of how IKEv2 is used with EAP. That section states the following when a different identity (IDi) is used in message 2 IKE_AUTH from initiator to responder, eg anonymous@realm, and realId@realm used in EAP identity response: When the initiator authentication uses EAP, it is...
I am working on ssl client because of some server update I was enabling the cipher TLS_DHE_RSA_WITH_AES_128_GCM_SHA256. While handshake with server I was facing Bad Record MAC Alert message from the server. I was verified the time stamp and encryption status that are correct. That doesn't make any problem. I have no id...
I am using AES-GCM to encrypt some data. I want every encryption to be done with a new random iv. For every encryption a new iv is generated and appended to the encrypted text to produce the cipher. Since the iv would be send in plaintext I thought I could also generate a HMAC of the iv and the encrypted text and appen...
Stream ciphers use a deceptively simple mechanism: you combine the plaintext data, bit by bit, with “key” bits, using the exclusive or operation. Why can't I use other opeartions such as NAND, AND, OR . Can you guys give me one real time example which brings advantage of using XOR over other operations.
Fix an interactive proof system $(P,V)$ and denote by $(P_k,V_k)$ an interactive proof system in which the parties play in parallel $k$ copies of $(P,V)$ and for which $V_k$ accepts if and only if $V$ would have accepted in all $k$ copies. The Parallel Repetition Theorem says that given a prover $P$ and input $x$ to th...
According to sources that I've read, it says that DES is not suited to a software implementation and that it is better suited to hardware, what does this mean?
I have a 1024-bits modulus n, the key d which is 1022 bit long, public exponent 65537, two factor p and q, and the ciphertext y 1023 bits which is all in numbers. How can we perform decryption and work out the plaintext? I have tried CrypTool, tried entering the key d, two factor p and q, but it always give me an err...
The secret key of BFV, BGV schemes is generated as a random ternary polynomial from R2 ( R2 is the key distribution used to sample polynomials with integer coefficients in {−1,0,1}) Is there any specific reason for it to be a ternary polynomial? can we have it as polynomial from Rq i.e integer coefficients from {0, 1, ...
I am reading this explanation of zkSnarks written by Maksym Petkus - Why and How zk-SNARK Works They work through the concept of zkSnarks using a polynomial which the prover knows & he has to convince the verifier that he knows it. The verifier knows that the polynomial has 2 factors ($x = 1$ & $x = 2$), he doesn't kno...
Trying to decrypt RSA Ciphertext with a private key using OpenSSl Used rsatool to generate a .pem file for private key which is 1022 bit long. Converted the original cyphertext 1023 bits long from just numbers to hex values of bytes I have used the command: openssl pkeyutl -decrypt -in C:\Users\abc\Desktop\Cypher.txt -...
This problem is related to Fields in Cryptography, My Question is why there is no multiplicative inverse for 2, isn't it 0.5?? or matters are diffrent if it was related to galois field ? I don't quite understand. This is the Addition Tabel... This Is the Multiplication Tabel... And this is the tabel with the additive...
Modulus n = 1024 bit p * q = 1024 bit phi_n = (p-1)*(q-1) = 1024 bit When calculating key d the multiplicative inverse d = inverse_mod(e, phi_n) The result of d is 1022 bit long instead of 1024 bit long, which is stopping me to decrypting the cyphertext of 1023 bit, the calculation is done in sagemath, where am I doing...