instruction stringlengths 15 30k |
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I am on cryptography course and there is a homework question to show that Hill cipher doesn't have perfect security.
So assume we have an cryptosystem $(P,C,K)$, where $P = C = \mathbb Z_{26}^N$ and $K$ is the set of invertible $N \times N$-matrices modulo $26$. Now we also have some probability distribution on $P$ ... |
This problem (i.e. generating a second preimage) is analyzed in the paper ["A generalized birthday problem"][1][[Citeseer]][2][[Slides]][3], by David Wagner, Crypto 2002.
If you add 8 public keys then the attack requires somewhere around $2^{64}$ hash computations, if you add 16 public keys before hashing them then... |
Alice and Bob are playing Rock-paper-scissors.
[Alice chooses a (a=stone,paper or scissors) and a nonce RA used as symmetric key for encryption]
A → B : A, RA(a)
[Bob chooses b (b=stone,paper or scissors)and nonce RB]
B → A : B, RB(b)
A → B : A, RA
[Now Bob decodes RA(a) and knows a and so he knows wh... |
Let's assume that we have a secure PRNG. Is it "safe" to initialize it with password, or seed based on a password like SHA256(password)?
If yes, is it "safe" to generate an RSA or DSA key from it?
-----------------
The idea behind this is to initialize a PRNG with a password, then use it to generate RSA or DSA... |
A system is used to securely store account numbers.
When an account number is added to the system it is securely encrypted and stored in a database along with the IV and a reference to the encrypted record is returned (so that the encrypted record can be retrieved at a later date).
If a second request for an ide... |
Alice and Bob are playing Rock-paper-scissors.
Alice chooses $a \leftarrow\{stone, paper, scissors\}$ and a nonce $R_A$ used as symmetric key for encryption
$$A → B : A, R_A(a)$$
Bob chooses $b \leftarrow\{stone,paper or scissors\}$ and nonce $R_B$
$$B → A : B, R_B(b)$$
$$A → B : A, R_A$$
Now Bob deco... |
One possibility for what you might be missing: normally the same key (the same matrix) is re-used to encrypt many messages. So now try counting the total entropy in $M$ length-$N$ messages, and the entropy in a $N\times N$ matrix, and compare what happens when $M$ gets large....
Another possibility you might be mis... |
Alice and Bob are playing Rock-paper-scissors.
Alice chooses $a \leftarrow\{stone, paper, scissors\}$ and a nonce $R_A$ used as symmetric key for encryption
$$A → B : A, R_A(a)$$
Bob chooses $b \leftarrow\{stone,paper, scissors\}$ and nonce $R_B$
$$B → A : B, R_B(b)$$
$$A → B : A, R_A$$
Now Bob decode... |
So I'm trying to understand the complexity of the biclique attack on Grostl and I have some questions:
1) The paper introduces sliced bicliques where on Grostl one constructs a biclique of dimension 1 and accordingly, we get 4 $Q's$ at state#5 and 4 $P's$ at state#8. What I understood is that each pair of $Q's$ shou... |
Does anyone know if there exists a PRG construction which takes as input an (RSA-sized) integer seed and outputs a fixed number of bits? There are number-theoretic PRGs such as the RSA, Micali-Schnorr, and BBB algorithms (see http://cacr.uwaterloo.ca/hac/about/chap5.pdf), but these require one to know both the seed and... |
I am wondering what concrete functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computable in the fo... |
One-way permutation over a small interval? |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I have a client a server communicating with messages encrypted using RSA.
Client knows server's public key, but server does not know client's public key. Is it possible to securely receive client's public key over network (without man in the middle intercepting and changing the key).
I was thinking that the clien... |
Securely send public key from client to server in RSA? |
I have a client and a server communicating with messages encrypted using RSA.
Initially, the client knows server's public key, but the server does not know the client's public key. Is it possible to securely receive the client's public key over a network (i.e. without a man in the middle intercepting and changing th... |
I am studying one time pad and find it hard to understand. What happens if the key is one bit or 100 bits shorter than the message? |
Why does a key have to be at least as long as a message (cryptography)? |
There are some [known groups][1] in which [computational Diffie-Hellman][2] assumption is equivalent to [discrete logarithm problem][3]. Besides, It has been shown that the equivalence holds "[when a small amount of extra information depending on the group order is provided][4]". Furthermore, those extra informations h... |
Why does a one-time-pad key have to be at least as long as a message? |
So I'm trying to understand the complexity of the [biclique attack on Grostl][1] and I have some questions:
1) The paper introduces sliced bicliques where on Grostl one constructs a biclique of dimension 1 and accordingly, we get 4 $Q's$ at state#5 and 4 $P's$ at state#8. What I understood is that each pair of $Q's$... |
I've been looking at the definition of a PRG, [here](https://en.wikipedia.org/wiki/Pseudo_random_number_generator#Mathematical_definition). This is a broader notion than a cryptographically secure PRG ("CSPRG"), which is described [here](http://en.m.wikipedia.org/wiki/Cryptographically_secure_pseudorandom_number_gener... |
Schneier [says][1]:
> Fewer and smaller S-boxes. It may be possible to reduce the number of
> S-boxes from four to one. Additionally, it may be possible to overlap
> entries in a single S-box: entry 0 would consist of bytes 0 through 3,
> entry 1 would consist of bytes 1 through 4, etc. The former
> simplificati... |
I'm reading the paper “[Collision-Resistant Hashing? Towards Making UOWHFs Practical][1]” , which compared TCR (Target Collision Resistant) and ACR (Any collision Resistant). It says
> we wish to stress one important practical advantage of TCR over ACR: because $x$ must be specified before $K$ is known, birthday att... |
Are the proofs based on a PRF assumption still valid when using a variable-length input PRF ?
The answer might be obvious, but I have a doubt. |
Right now I'm using a simple padding system that takes the plaintext, hashes it with SHA512, and appends $x$ bytes of the hash as padding where $x$ is the delta between the plaintext and nearest blocksize multiple.
Is this considered a secure method of padding the message? I am also authenticating the encrypted data... |
I would like to insert a key deriving function into EAX mode, in order to hamper brute-force attacks for a key-size restricted cipher (56 bits). The modification inserts an identical multi-block pattern $S$ behind the corresponding tweaks:
Original: $OMAC(T||...)$ where the 128-bit tweak $T$ is either `0`, `1`, `2`.... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
In regards to the protections implemented in OpenSSL 0.9.6d (described in section 2. http://www.openssl.org/~bodo/tls-cbc.txt). My understanding is that the mechanism prepends an empty record when sending data in order to make the IV unpredictable. however the client->server and server->client maintain separate IV data... |
I want to know whether I can break RSA (textbook) with known plaintext/ciphertext attacks.
**Known plain-text**
Let d be the decrypted message and m the plaintext message.
d = (m)^a mod n
Since all I have is the plain and ciphertext, all I could do here is guess the decryption exponent "a" until I find one ... |
I'm not exactly certain what answer you're looking for; I tried to cover all the obvious bases.
Actually, with RSA, we generally assume that the attacker knows the public key (the modulus $n$ and the public exponent $e$); with that, he can generate encrypt as much plaintext (by selecting a value $M$ and computing $M... |
I want to know whether I can break RSA (textbook) with known plaintext/ciphertext attacks.
**Known plain-text**
Let $c$ be the ciphertext and $m$ the plaintext.
$$c = m^a \mod n$$
Since all I have is the plain and ciphertext, all I could do here is guess the decryption exponent $a$ until I find one that lea... |
I'm not exactly certain what answer you're looking for; I tried to cover all the obvious bases.
Actually, with RSA, we generally assume that the attacker knows the public key (the modulus $n$ and the public exponent $e$); with that, he can encrypt as much plaintext as he cares to (by selecting a value $M$ and comput... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I've done some reading about implementing AES256 and deriving a key from a password. If I understand correctly:
- I want to generate a new salt (for the key) and a new IV (for the encrypted message) for every new message.
- It should also not be a problem sending the salt and the IV together with the message.
I... |
Given $$e(g, d) = c $$
where,
- $e$ is bilinear pairing function chosen by the user/attacker,
- the values of $g$ and $c$ are known
- $g, d ∈ \mathbb{G}_1$ , $c$ depends upon the $e$
can we somehow compute the value of $d$
In a high level, I am asking if there exists a function $f$ that, in one way is... |
I am designing a vault that tokenizes a plaintext that consists of 6 decimal digits, with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new random index.
If it does exist it returns the same index it had returned b... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
(This question is related to homework)
I am doing a cryptography course via long distance and we have been given an assignment which is based on lattice-based cryptography. I have spent the majority of the past week sifting through papers and videos in an attempt to build my understanding of the subject, but due to th... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am doing a cryptography course via long distance and we have been given an assignment which is based on lattice-based cryptography. I have spent the majority of the past week sifting through papers and videos in an attempt to build my understanding of the subject, but due to the intensely technical manner in which ... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
I am wondering what concrete computable functions we know that
- are a **permutation** over an integer **interval** of parameterizable size $s$, for relatively small $s$ starting circa $2^{64}$, to perhaps $2^{256}$; without loss of generality we'll translate the interval to $\{0\dots s-1\}$;
- are easily computabl... |
In the paper "[Multiparty Computation Secure Against
Continual Memory Leakage][1]", on page 1241 (that's page 7 of the PDF) under section 2.3, the authors discuss "The Election Protocol" that they use to elect committees. The election protocol they use guarantees a constant fraction of honest parties and that each co... |
Why do authors execute a leakage resilient election protocol inside a leak-free phase? |
I understand the concept of a *Zero Knowledge Proof* thanks to the easy to understand analogy of Alibaba's cave. However, this seems to require interaction between the verifier and the other party.
I have not found an explanation of **non-interactive** zero knowledge proofs (NIZK). The wikipedia article is way too c... |
What is a Non-Interactive Zero Knowledge Proof? |
I am designing a vault that tokenizes credit card numbers (a plaintext that consists of 16 decimal digits), with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new random index.
If it does exist it returns the same ... |
- It depends on *how long* you want to keep your data safe for. Do you
want the secret safe for 1 week, the rest of your life or forever? Will you get in trouble, put in prison or be killed if that secret is revealed to the wrong person?
- It also depends on *who* you want to keep the data safe *from*. Do you wa... |
I am designing a vault that tokenizes credit card numbers (a plaintext that consists of 16 decimal digits), with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new random index.
If it does exist it returns the same ... |
Suppose I wanted to add explicit key confirmation to Diffie-Hellman key exchange, would the following scheme be secure?
1. Alice selects a random $a$ and sends $g^a \mod p$ to Bob
2. Bob selects a random $b$, computes the shared secret $S = (g^a \mod p)^b$
3. Bob computes two keys using HKDF ($H(k, m)$ denotes... |
I want to represent a Montgomery Curve (curve25519) in Weierstrass form as a personal exercise.
After doing some math and referencing the conversion equation at http://en.wikipedia.org/wiki/Montgomery_curve, several of my terms contain decimals, which I believe is incorrect. Namely,
(3-A^2) / (3*B^2)
is a de... |
What are some restrictions when converting Montgomery Curves into Weierstrass Curves? |
You are looking for almost-prime-order cyclic groups $G$ of order $n$ that have an easily computed bijection $G \rightarrow \{0,1,2,\dots,n-1\}$, along with an estimate of how quickly discrete logarithms can be computed in $G$.
There seems to be two choices, a subgroup of $\mathbb{F}_p^*$ with $(p-1)/2$ prime, and t... |
My comment already gave you the answer; I'm submitting an official answer to give you something to upvote :-)
An elliptic curve is defined within a field; in the case of curve25519, it is defined within the field $GF(2^{255}-19)$; this is a prime field, because $2^{255}-19$ is prime.
So, when we get to the conv... |
My comment already gave you the answer; I'm submitting an official answer to give you something to upvote :-)
An elliptic curve is defined within a field; in the case of curve25519, it is defined within the field $GF(2^{255}-19)$; this is a prime field, because $2^{255}-19$ is prime.
So, when we get to the conv... |
I'm also afraid you couldn't understand this as D.W., but let us start.
I sometimes cannot understand your questions. Please restate them, if possible.
# The definition of the Ajtai hash functions
Let $n$, $m$, and $q$ be positive integers.
Let $R = \mathbb{Z}_q$ be the quotient ring of integers modulo $q$.
Le... |
My comment already gave you the answer; I'm submitting an official answer to give you something to upvote :-)
An elliptic curve is defined within a field; in the case of curve25519, it is defined within the field $GF(2^{255}-19)$; this is a prime field, because $2^{255}-19$ is prime.
So, when we get to the conv... |
You are looking for almost-prime-order cyclic groups $G$ of order $n$ that have an easily computed bijection $G \rightarrow \{0,1,2,\dots,n-1\}$, along with an estimate of how quickly discrete logarithms can be computed in $G$.
There seems to be two choices, a subgroup of $\mathbb{F}_p^*$ with $(p-1)/2$ prime, and t... |
You are looking for almost-prime-order cyclic groups $G$ of order $n$ that have an easily computed bijection $G \rightarrow \{0,1,2,\dots,n-1\}$, along with an estimate of how quickly discrete logarithms can be computed in $G$.
There seems to be two choices, a subgroup of $\mathbb{F}_p^*$ with $(p-1)/2$ prime, and t... |
I've done some reading about implementing AES256 and deriving a key from a password. If I understand correctly:
- I want to generate a new salt (for the key) and a new IV (for the encrypted message) for every new message.
- It should also not be a problem sending the salt and the IV together with the message.
I... |
I am working on an android project for school and I am supposed to do a DHKE(Diffie Hellman Key Exchange). Everything works well, the problem is that it takes a lot of time (really a lot) to generate DHParameters. Basically, in my code, this is the part that is the most time (and battery) consuming:
KeyPairGener... |
I have a stream of data originating in some physical phenomena that may expose random behavior (due to quantum effects, thermal noise, the butterfly effect in chaotic dynamical systems, etc). The stream may carry some amount of entropy (true randomness), but it may be distributed unevenly throughout the stream and its ... |
I am working on an android project for school and I am supposed to do a DHKE(Diffie Hellman Key Exchange). Everything works well, the problem is that it takes a lot of time (really a lot) to generate DHParameters. Basically, in my code, this is the part that is the most time (and battery) consuming:
KeyPairGener... |
I am working on an Android project for school and I am supposed to do a DHKE (Diffie Hellman Key Exchange). Everything works well. The problem is that it takes a lot of time (really a lot) to generate DHParameters. Basically, in my code, this is the part that is the most time (and battery) consuming:
KeyPairGen... |
I have a potentially infinite stream of data originating in some physical phenomena that may expose random behavior (due to quantum effects, thermal noise, the butterfly effect in chaotic dynamical systems, etc). The stream may carry some amount of entropy (true randomness), but it may be distributed unevenly throughou... |
I have a potentially infinite stream of data originating in some physical phenomena that may expose random behavior (due to quantum effects, thermal noise, the butterfly effect in chaotic dynamical systems, etc). The stream may carry some amount of entropy (true randomness), but it may be distributed unevenly throughou... |
Is there a way to authenticate users online without knowing their real identity yet preventing them from registering twice? If not, what is the least amount of information you would need? Suppose the user has a smart phone and you have access to all its sensors for biometric purposes. Probabilistic guarantees are quite... |
Is there a way to authenticate users online without knowing their real identity yet preventing them from registering twice? If not, what is the least amount of information you would need? If it helps, you may assume the user has a smart phone and you have access to all its sensors. Probabilistic guarantees are quite ac... |
We're building a stateless RESTful API that relies on the content of OAuth2 tokens to identify users and what they have access to. Users authenticate with other means and are given a token, which they then use to authenticate API requests for an hour or so till it expires.
Since we want it to be stateless, we can't ... |
I am designing a vault that tokenizes credit card numbers (a plaintext that consists of 16 decimal digits), with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new index.
If it does exist it returns the same index i... |
I am designing a vault that tokenizes credit card numbers (a plaintext that consists of 16 decimal digits), with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new index.
If it does exist it returns the same index i... |
I am designing a vault that tokenizes credit card numbers (a plaintext that consists of 16 decimal digits), with the following requirements:
1. Given some plaintext, the vault returns an index.
If the plaintext does not exist it returns a new index.
If it does exist it returns the same index i... |
Let $ f : \{0,1\}^* \rightarrow \{0,1\}^n$ and $ g : \{0,1\}^* \rightarrow \{0,1\}^n$. h is created by concatenate f and g: $ h : \{0,1\}^* \rightarrow \{0,1\}^{n+m}$ with h(x) = f(x) || g(x). How do I prove that both f and g must be preimage resistance if h is to be preimage resistance ? Is the same true for 2nd-preim... |
How to determine which type of crypto is used in a text file? |
Let $ f : \{0,1\}^* \rightarrow \{0,1\}^n$ and $ g : \{0,1\}^* \rightarrow \{0,1\}^n$. $h$ is created by concatenate f and g: $ h : \{0,1\}^* \to \{0,1\}^{n+m}$ with $h(x) = f(x) || g(x)$. How do I prove that both $f$ and $g$ must be preimage resistant if h is to be preimage resistant? Is the same true for 2nd-preimage... |
Let $ f : \{0,1\}^* \rightarrow \{0,1\}^n$ and $ g : \{0,1\}^* \rightarrow \{0,1\}^n$. $h$ is created by concatenate f and g: $ h : \{0,1\}^* \to \{0,1\}^{n+m}$ with $h(x) = f(x) || g(x)$. How do I prove that both $f$ and $g$ must be preimage resistant if $h$ is to be preimage resistant? Is the same true for 2nd-preima... |
I am trying to implement elliptic curve point addition in hardware for NIST p256 and p384 curves. I have noticed the following issue with the suggested NIST routines:
Routine 2.2.7 of http://www.nsa.gov/ia/_files/nist-routines.pdf point addition R= S + T is not valid for the case S = T ( this would be a point doubli... |
Safe elliptic curve point addition using projective coordinates: How do I tell if the points are the same? |
I am trying to implement elliptic curve point addition in hardware for NIST p256 and p384 curves. I have noticed the following issue with the suggested NIST routines:
Routine 2.2.7 of http://www.nsa.gov/ia/_files/nist-routines.pdf point addition $R = S + T$ is not valid for the case $S = T$ ( this would be a point d... |
Unified addition means that the formula you use for adding two points doesn't depend on whether they are equal. Simplifying [point addition in the Weierstrass form](http://en.wikipedia.org/wiki/Elliptic_curve#The_group_law) somewhat $s=(y_A-y_b)/(x_A-x_b)$ when $A\neq B$ - this is "Adding". Otherwise $s=(3x_A^2-p)/{2y_... |
Are there digital signatures for which, given two documents signed by the same key, one could derive the key?
With such one-time signatures, one may be able to design a cryptocurrency based on proof-of-stake instead of proof-of-work. To disincentivise miners from cheating by mining several blocks, one could impose t... |
This is my PKCS#5 & AES/ECB Python 3.3 code:
from Crypto.Cipher import AES
def encrypt_snap(media):
key = bytes('M02cnQ51Ji97vwT4', 'utf8')
cipher = AES.new(key, AES.MODE_ECB)
padded = media + ((16 - len(media) % 16) * chr(16 - len(media) % 16))
encrypted = cipher.e... |
Is the random data at the end of my decrypted message supposed to be there? |
First, I am no crypto expert although I am doing the MOOC.
I have an item which has as id: uuidv4
When I create this item:
1. I create a new uuidv4
2. check if it already exists
3. and if not, I store it in the db.
Now this item can be deleted. So lets say that there could be a conversation 'about' thi... |
You know, technically an uuidv4 is already designed to be unique. That's what it's for. In other words, the probability of you generating the same uuidv4 is supposed to be virtually zero. So why are you checking for duplicates?
The whole point of uuid's is to make sure nobody ever gets assigned the same one even if ... |
I want to implement brute force hacking using RSA. How to simulate and measure time duration? What software/simulator is needed? Please help me. |
How to simulate and measure brute force hacking using RSA? Please help me |
I want to implement brute force hacking using RSA. How can I simulate and measure time duration? What software/simulator is needed? Please help me. |
How can I simulate and measure brute force hacking using RSA? |
RSA assumption: When $c = m^e \mod N$, finding $m$ (when we know $c$, $e$ and $N$ is hard )
Is there an algorithm that could use $c, e, N$ to find $m$ easily for any $c$?
|
Let $ f : \{0,1\}^* \rightarrow \{0,1\}^n$ and $ g : \{0,1\}^* \rightarrow \{0,1\}^m$. $h$ is created by concatenate f and g: $ h : \{0,1\}^* \to \{0,1\}^{n+m}$ with $h(x) = f(x) || g(x)$. How do I prove that both $f$ and $g$ must be preimage resistant if $h$ is to be preimage resistant? Is the same true for 2nd-preima... |
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