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I'm currently implementing, with `crypto++`, and AES tranmsission system, whose `key` is based on a previous `MasterSecret` of 256 bits (which has been expanded using PBKDF2).
This `MasterSecret` is then split into a `key` and an `iv`, to encrypt a message using `AES-GCM`.
I **must** work with AES-256, so my key ... |
Can file-versioning, which is available for instance in Dropdox, weaken the security of encrypted files if someone is able to see two or more snapshots of the ciphertext at different times?
To be specific, the files are encrypted by PGP on the file level (each file, making extension: important.doc.pgp ) with asymmet... |
For example, in Don Boneh et al.'s paper "[Evaluating 2-DNF Formulas on Ciphertexts][1]", they gave an encryption system that the cihpertext can be in either $G$ (when only additional homomorphic operations are evaluated on the ciphertext) or $G_1$ (when one multiplication applies). In such a setting, is it possible to... |
In bilinear pairings, is it possible to let someone be only able to decrypt ciphertexts in $G_1$ but not able to decrypt the ciphertexts in $G$? |
The Secure Remote Password (SRP) protocol lets a client prove to a server that it knows a specific password without revealing that password to the server. The server stores a cryptographic verifier for the user account. If an attacker impersonates as the server it cannot learn the user's password.
Now, does it also... |
Does SRP also authenticate the server to the client? |
Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values. We compute four values as below:
1) $u_1=r_1\cdot x,\ \ u_2=r_1\cdot z$
2) $w_1=r_2\cdot x,\ \ w_2=r_2\cdot z$
**Question**: D... |
Do $u_1=r_1\cdot x,\ \ u_2=r_1\cdot z, w_1=r_2\cdot x,\ \ w_2=r_2\cdot z$ Leak Information? |
The following encryption scheme: choose a random string $r \leftarrow \{0,1\}^n$ and compute the ciphertext $c= \thinspace <c_0, c_1>= \thinspace <r, F_k(r) \oplus m>$, assuming $F$ a PRF; is _CPA-secure_, as we have a randomized/non-deterministic encryption process. Why, if applying a modified encryption process, i.e.... |
Consider a multi-part message m= m0, m1, m2,....., mn.
We need to verify individual parts of the message or combination of parts.
Of course, we can sign each part and then verify individually. But that is not an efficient solution.
Are there any efficient solution/ scheme for this problem? |
Does $(u_1=r_1\cdot x,\ \ u_2=r_1\cdot z, \ \ w_1=r_2\cdot x,\ \ w_2=r_2\cdot z)$ Leak Information? |
For example, in Don Boneh et al.'s paper "[Evaluating 2-DNF Formulas on Ciphertexts][1]", they gave an encryption system that the cihpertext can be in either $G$ (when only additional homomorphic operations are evaluated on the ciphertext) or $G_1$ (when one multiplication applies). In such a setting, is it possible to... |
The Secure Remote Password (SRP) protocol lets a client prove to a server that it knows a specific password without revealing that password to the server. The server stores a cryptographic verifier for the user account. If an attacker impersonates as the server it cannot learn the user's password.
Now, does it also... |
I am thinking on a simple symmetric stream cipher. My first idea is the following:
* The key is a set of array of random bytes ($\underline{k}_1$ ... $\underline{k}_n$), whose length is $l_1$, $l_2$, ..., $l_n$ (any pair of $l_j$, $l_k$ is relative prime).
* We encrypt/decrypt the $i$-th byte of the stream by XOR-r... |
Symmetric stream cipher, is it known? |
I am thinking on a simple symmetric stream cipher. My first idea is the following:
* The key is a set of array of random bytes ($\underline{k}_1$ ... $\underline{k}_n$), whose length is $l_1$, $l_2$, ..., $l_n$ (any pair of $l_j$, $l_k$ is relative prime).
* We encrypt/decrypt the $i$-th byte of the stream by XOR-r... |
I looked everywhere on the web and I did find a lot of information about full disk encryption, but nothing really answered my question.
When formatting a partition to use LUKS, the two most common ciphers are
- aes-xts-plain64
- aes-cbc-essiv:sha256.
Now I know that ESSIV is simply a way to prevent the wate... |
I am thinking on a simple symmetric stream cipher. My first idea is the following:
* The key is a set of array of random bytes ($\underline{k}_1$ ... $\underline{k}_n$), whose length is $l_1$, $l_2$, ..., $l_n$ (any pair of $l_j$, $l_k$ is relative prime).
* We encrypt/decrypt the $i$-th byte of the stream by XOR-r... |
We all know that MD5's collision resistance is severly broken.
But when thinking of "random" strings with great cryptographic importance I've come up with NIST's curve seeds and MD5 collisions. But for this to really work out I'd need the most famous MD5 collision.
So I'm asking: **What is the most famous MD5 col... |
What was the first MD5 collision ever constructed? |
Consider a multi-part message $m = (m_0, m_1, m_2, \dots, m_n)$.
We need to verify individual parts of the message or combination of parts.
Of course, we can sign each part and then verify them individually. But that is not an efficient solution.
Is there any efficient solution / scheme for this problem? |
Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values. We compute four values as below:
1) $u_1=r_1\cdot x,\ \ w_1=r_1\cdot z$
2) $u_2=r_2\cdot x,\ \ w_2=r_2\cdot z$
**Question**: D... |
Is it secure to use the same RSA private key to sign many messages (roughly $10^{6}$) via PKCS#11 mechanism `CKM_SHA256_RSA_PKCS` using a reasonably long (i.e. 2048 bit) key?
Assume all messages and their signatures are available to the attacker.
For reference the `CKM_SHA256_RSA_PKCS` mechanism is described as f... |
Limit the number of private key uses for RSASSA-PKCS1-v1_5 with SHA-256 signature? |
Is there a practical security difference between *“OTP with letters”* and *“OTP with numbers”*?
If, for example, I encrypt a letter message using Tabula Recta with a random letter key, I would get:
THISI SATES TXAAA - message
MOSSK VFXNN EJRQW - OTP key
FVAKS NFQRF XGRQW - cipher
Would such encry... |
Assuming all messages and their signatures are available to the attacker, is it secure to use the same RSA private key to sign many messages (roughly $10^{6}$) via PKCS#11 `CKM_SHA256_RSA_PKCS` using a reasonably long (i.e. 2048 bit) key?
For reference, `CKM_SHA256_RSA_PKCS` is described as follows:
> The PKCS #1... |
Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values.
We compute four values as below:
1. $u_1=r_1\cdot x,\ \ w_1=r_1\cdot z$
2. $u_2=r_2\cdot x,\ \ w_2=r_2\cdot z$
**Question**: ... |
When I read papers, I often see the comments, "order-preserving encryption is deterministic and it is not IND-CPA secure", or in general "it is not secure enough to be implemented in practice". So I am wondering if these comments are correct especially from the practical implementation's point of view. I know a lot of ... |
Is it secure to use order preserving encryption in practice? |
I have quite a few WinRAR volumes that are all encrypted with the same password. The password is long and unbruteforceable, but I recently read that WinRAR uses PBDKF2 as its key-derivation function instead of generating a new volume key every time like TrueCrypt, which means that in essence all of these volumes have t... |
Attacks on WinRAR volumes reusing same password? |
Just started learning about Cryptography and Network Security in general, and I can't seem to grasp the understanding of the following question. Please correct me if I am misunderstanding anything.
Imagine that there exists a Pseudorandom Generator that simply doubles all key length, `G(n) = {0,1}^n -> {0,1}^2n`. I... |
Is it possible to implement any of the 5 modes of operation (ECB, CBC, OFB, CFB, CTR) with a hash function?
Thanks,
Mark |
Is base64 the best two-way hash function to encrypt and trasmit a set of integer numbers via Internet? |
So let's say we use a cipher suite with DH key exchange and AES symmetric encryption.
Alice and Bob both end up with the same shared secret key `k`.
How is this value `k` used in e.g. AES?
Will it be hashed before use? Is there a PBKDF involved? And what do we do about small `k` (e.g. 10, ..) |
TLS: How is the shared secret (via Diffie-Hellman) used in the symmetric crypto function? |
The RAR5 archive format encrypts file data using AES in CBC mode, and generates a 256-bit key using PBDKF2-HMAC-SHA256 (32768 iterations default?).
If an attacker is able to view many files encrypted this way all with the same key, the attack is to recover the key from the ciphertext. This is not an easy task, even ... |
So let's say we use a cipher suite with DH key exchange and AES symmetric encryption. Alice and Bob both end up with the same shared secret key $k$.
How is this value `k` used in e.g. AES? Will it be hashed before use, or is there a PBKDF involved? And what do we do about small $k$ (e.g. $10, …$) |
I am new to crypto and wondered what would happen when we encrypt twice using any algorithm and the same key.
Consider two block ciphers A and B.
We generate the ciphertext as c = A(B(m)) for any message m.
If they are in the same message space and they map to the same ciphertext space, why would using the same key ... |
Is it possible to implement any of the 5 modes of operation (ECB, CBC, OFB, CFB, CTR) with a hash function? |
Does $(u_1=r_1\cdot x,\ \ w_1=r_1\cdot z, \ \ u_2=r_2\cdot x,\ \ w_2=r_2\cdot z)$ Leak Information? |
We've construct a new private RSA key from two known private RSA keys $Priv_1$ and $Priv_2$ as follows:
$$p = next\underline{}prime\left(\frac{Priv_1(p) + Priv_2(p)}{2}\right)$$
and
$$q = next\underline{}prime\left(\frac{Priv_1(q) + Priv_2(q)}{2}\right)$$
where $Priv_{1}(p)$ is the first factor of $Priv_1$ and so o... |
We've constructed a new private RSA key from two known private RSA keys $Priv_1$ and $Priv_2$ as follows:
$$p = next\underline{}prime\left(\frac{Priv_1(p) + Priv_2(p)}{2}\right)$$
and
$$q = next\underline{}prime\left(\frac{Priv_1(q) + Priv_2(q)}{2}\right)$$
where $Priv_{1}(p)$ is the first factor of $Priv_1... |
Consider a practical scenario as described in Microsoft's [Expand Export a Certificate with the Private Key][1]. We can see a certificate with private key can be exported as a PKCS #12 file, where the private key can be protected by a password (in Step 7).
Question 1: If one day this PKCS #12 file is stolen by a ha... |
Is it not secure if we use weak passwords to protect exported PKCS #12 files with private keys? |
We've constructed a new private RSA key from two known private RSA keys $Priv_1$ and $Priv_2$ as follows:
$$p = next\underline{}prime\left(\frac{Priv_1(p) + Priv_2(p)}{2}\right)$$
and
$$q = next\underline{}prime\left(\frac{Priv_1(q) + Priv_2(q)}{2}\right)$$
where $Priv_{1}(p)$ is the first factor of $Priv_1... |
Consider a practical scenario as described in Microsoft's [Expand Export a Certificate with the Private Key][1]. We can see a certificate with private key can be exported as a PKCS #12 file, where the private key can be protected by a password (in Step 7).
Questions:
1. If one day this PKCS #12 file is stolen by... |
The simple way to iterate a hash function $H(H(m))$ only makes brute force preimage finding slower, but leaves collision attacks as fast since a collision in the inner hash function is a collision in the overall function.
Is there an iterative algorithm that also slows down brute force collision attacks? Without exp... |
I want to de/encrypt several binary files rather frequently on a normally battery-powered device. My goal is to use AES-256 when the device is AC-powered and a highly performant algorithm when it's battery-powered to save power. I appreciate that the level of security will be compromised.
Is there a performant algo... |
Problem re-statement and notations: we know three 2048-bit RSA public moduli $N_1$, $N_2$, $N$, of unknown factorizations $N_1=p_1\cdot q_1$, $N_2=p_2\cdot q_2$, $N=p\cdot q$, with $p_1<q_1$, $p_2<q_2$. We additionally know that $p$ is the smallest prime at least $(p_1+p_2)/2$, and $q$ the smallest prime at least $(q_1... |
Problem re-statement and notations: we know three 2048-bit RSA public moduli $N_1$, $N_2$, $N$, of unknown factorizations $N_1=p_1\cdot q_1$, $N_2=p_2\cdot q_2$, $N=p\cdot q$, with $p_1<q_1$, $p_2<q_2$. We additionally know that $p$ is the smallest prime at least $(p_1+p_2)/2$, and $q$ the smallest prime at least $(q_1... |
Problem re-statement and notations: we know three 2048-bit RSA public moduli $N_1$, $N_2$, $N$, of unknown factorizations $N_1=p_1\cdot q_1$, $N_2=p_2\cdot q_2$, $N=p\cdot q$, with $p_1<q_1$, $p_2<q_2$. We additionally know that $p$ is the smallest prime at least $(p_1+p_2)/2$, and $q$ the smallest prime at least $(q_1... |
Problem re-statement and notations: we know three 2048-bit RSA public moduli $N_1$, $N_2$, $N$, of unknown factorizations $N_1=p_1\cdot q_1$, $N_2=p_2\cdot q_2$, $N=p\cdot q$, with $p_1<q_1$, $p_2<q_2$. We additionally know that $p$ is the smallest prime at least $(p_1+p_2)/2$, and $q$ the smallest prime at least $(q_1... |
Problem re-statement and notations: we know three 2048-bit RSA public moduli $N_1$, $N_2$, $N$, of unknown factorizations $N_1=p_1\cdot q_1$, $N_2=p_2\cdot q_2$, $N=p\cdot q$, with $p_1<q_1$, $p_2<q_2$. We additionally know that $p$ is the smallest prime at least $(p_1+p_2)/2$, and $q$ the smallest prime at least $(q_1... |
We can sign the whole message and verify it.
That is an efficient solution.
RSA signature or DSA is better for this? |
> If one day this PKCS #12 file is stolen by a hacker, then, can he perform an offline dictioary attack to this file?
Yes, that's possible. The password is simply used to directly derive a symmetric key, which is used in turn to encrypt the private key.
> Is the (un-)exportability guaranteed by a cryptography alg... |
Consider a multi-part message $m = (m_0, m_1, m_2, \dots, m_n)$.
We need to verify individual parts of the message or combination of parts.
Of course, we can sign each part and then verify them individually. But that is not an efficient solution.
Is there any efficient solution / scheme for this problem? |
Given a message $m$ that consists of several parts $m_0,\dots m_n$ we want to be able to verify individual parts or a combination thereof.
The simplest solution is independently signing each part. But since asymmetric signatures are relatively expensive to compute and verify, that might not be the most efficient app... |
Given a message $m$ that consists of several parts $m_0,\dots m_n$ we want to be able to verify individual parts or a combination thereof.
The simplest solution is independently signing each part. But since asymmetric signatures are relatively expensive to compute and verify, that might not be the most efficient app... |
Given a message $m$ that consists of several parts $m_0,\dots m_n$ we want to be able to verify individual parts or a combination thereof.
The simplest solution is independently signing each part. But since asymmetric signatures are relatively expensive to compute and verify, that might not be the most efficient app... |
Consider a multi-part message m= m0, m1, m2,....., mn.
We need to verify individual parts of the message or combination of parts.
Of course, we can sign each part and then verify individually. But that is not an efficient solution.
Are there any efficient solution/ scheme for this problem? |
Given a message $m$ that consists of several parts $m_0,\dots m_n$ we want to be able to verify individual parts or a combination thereof.
The simplest solution is independently signing each part. But since asymmetric signatures are relatively expensive to compute and verify, that might not be the most efficient app... |
The book *Cryptography Engineering* by Fergusun, Schneier, Kohno section 2.7.1 explains Birthday Attacks: "In general, if an element can take on N different values, then you can expect the first collision after choosing about sqrt(N) random elements." This is an approximation.
We are planning to upgrade the way we s... |
Yes! I'd recommend at least 64 bits, but that's only because powers of two are convenient and space is cheap. Furthermore, usually a salt of the block size of the hash you're using is usually best, because salting at all will almost always involve an extra block, so why not fill it up given that there will be no perfor... |
Consider we have a fixed value $x$. We pick values $ r_1,r_2,z\leftarrow \mathbb{F}_p$, where $p$ is a large prime number, and it is public. So $r_1,r_2,z$ are uniformly random values.
We compute four values as below:
1. $u_1=r_1\cdot x,\ \ w_1=r_1\cdot z$
2. $u_2=r_2\cdot x,\ \ w_2=r_2\cdot z$
**Question**: ... |
I find that for every 100 password salts in our database, we only average 94.73 distinct salt values. Is there a way to take that observation and calculate the amount of effective entropy (or whatever is the correct term) we have in our salts?
Clearly we need to improve how we generate salts. But, meanwhile, I'd lik... |
Is it possible to reverse the birthday attack calculation? |
I want to make this clear: You're defining $E_K(m):\{0,1\}^{2n}\times \{0,1\}^n\rightarrow \{0,1\}^{2n}$ as $E_K(m):=G(K)\oplus m$. This construction is well-known in the literature. It can't be CPA secure because it is a deterministic algorithm. However as discussed in Katz' and Lindell's book Introduction to Modern C... |
I find that for every 100 password salts in our database, we only average 94.73 distinct salt values. Is there a way to take that observation and calculate the amount of effective entropy (or whatever is the correct term) we have in our salts?
Clearly we need to improve how we generate salts. But, meanwhile, I'd lik... |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:43:47 UTC on the eprint archive server, with attribution to Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conf... |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:43:47 UTC on the eprint archive server, with attribution to Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conf... |
In what ways would you simplify? What would be changed to be more modern or extensible? Suppose you have no requirement to adapt to previous protocols. Links to proposed designs, existing protocols, as well as any ideas are welcome. |
If you were to design a PKI from scratch, what would you do? |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:43:47 UTC on the eprint archive server, with attribution to Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conf... |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:43:47 UTC on the eprint archive server, with attribution to Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conf... |
According to [wikipedia][1], a hash maps digital data of **arbitrary size** to digital data of **fixed size**.
For all practical measures, a hash is a unique signature of a big chunk of data. But there is such a thing as a collision free hash, [I "heard"][2].
Other than being able to decompress back, arguably the... |
Why can't we use a perfect hash to compress data reliably? |
When using advanced steganographic methods (like F5) what is the approximate maximum embedding rate when advanced Steganalysis (like a machine learning approach) can no longer reliably detect it?
I have searched for papers dealing with this topic but have been unable to find any. Does anyone here know anything abou... |
Minimum stenographic embedding rate not detectable by steganalysis? |
The book *Cryptography Engineering* by Fergusun, Schneier, Kohno section 2.7.1 explains Birthday Attacks: "In general, if an element can take on N different values, then you can expect the first collision after choosing about sqrt(N) random elements." This is an approximation.
We are planning to upgrade the way we s... |
Maximum stenographic embedding rate not detectable by steganalysis? |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:44 UTC on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conference. First two versi... |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:44 UTC on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2], during the Crypto 2004 conference. First two versi... |
According to [wikipedia][1], a hash maps digital data of **arbitrary size** to digital data of **fixed size**.
For all practical measures, a hash is a unique signature of a big chunk of data. But there is such a thing as a collision free hash, [I "heard"][2].
Other than being able to decompress back, arguably the... |
I find that for every 100 password salts in our database, we only average 94.73 distinct salt values (averaged over a total of around 18 million). Is there a way to take that observation and calculate the amount of effective entropy (or whatever is the correct term) we have in our salts?
Clearly we need to improve h... |
In the full-length proof of [PAK][1] scheme, the authors made extensive use of random oracles to extract (guessed) password from the messages generated by the real world adversary for the ideal world simulator.
Questions:
1. Are all the random oracle calls $H_i(\cdots)$ in the real world protocol (even called by ... |
Do random oracles are called even by honest users in the PAK protocol [BMK00]? |
According to [wikipedia][1], a hash maps digital data of **arbitrary size** to digital data of **fixed size**.
For all practical measures, a hash is a unique signature of a big chunk of data. But there is such a thing as a collision free hash, [I "heard"][2].
Other than being able to decompress back, arguably the... |
Why can't we use a hash with no collision to compress data reliably? |
As far as I can tell, the first web publication of an MD5 collision was on 17-Aug-2004 17:44 UTC (a few hours after the results where presented at the [Crypto 2004 Rump Session][1]), on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 a... |
The first publication of an MD5 collision was on 17-Aug-2004 17:44 UTC on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][2], [third version][3]. The results where fresh: the authors had just corrected IV endianness, that ... |
When using advanced steganographic methods (like F5) what is the approximate maximum embedding rate when advanced Steganalysis (like a machine learning approach) can no longer reliably detect it?
I have searched for papers dealing with this topic but have been unable to find any. Does anyone here know anything abou... |
Maximum steganographic embedding rate not detectable by steganalysis? |
The first publication of an MD5 collision was on 17-Aug-2004 17:44 UTC on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2]. The results where fresh: the authors had just corrected IV endianness, that ... |
The first publication of an MD5 collision was on 17-Aug-2004 17:44 UTC on the eprint archive server: Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu, [_Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD_][1], [third version][2]. The results where fresh: the authors had just corrected IV endianness, that ... |
Suppose we useLFSR, which gives output $x_1x_2x_3\dots$ from some particular initial state. From another state, different from previous, same LSFR though, it gives sequence $y_1y_2y_3\dots$
Intuitively for some $i$ inequality must hold truth $x_i\neq y_i$, but "intuitively" isnt exactly convincing, neither "empirica... |
Assume we have a Baretto Naehrig curve over $GF(p)$ and a field extension $GF(p^{12})$ given by a minimum polynomial. Let $G \in GF(p)$ and $Q \in GF(p^{12})$ from the trace 0 subgroup.
Do then the Reduced Tate and Ate pairings produce the same values? |
Are the values of Tate and Ate pairing the same? |
Given a message $m$ that consists of several parts. we want to be able to verify individual parts or a combination thereof.
The simplest solution is independently signing each part. But since asymmetric signatures are relatively expensive to compute and verify, that might not be the most efficient approach.
Is th... |
The IND-CPA game has two challenge-response phases
1) A key is generated by running $Gen(1^n)$ and challenger selects a bit
b {0,1} uniformly at random
2) Adversary gets input $1^n$
3) Can query the oracle a polynomial number of times with messages and gets $E_k(m)$ back
4) Attacker sends messages $m_0$, $... |
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