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The difference between the PKCS#5 and PKCS#7 padding mechanisms is the block size; PKCS#5 padding is defined for 8-byte block sizes, PKCS#7 padding would work for any block size from 1 to 255 bytes.
This is the definition of PKCS#5 padding (6.2) as defined in the RFC:
The padding string PS shall consist of 8 - (||M|| mod 8) octets all
having value 8 - (...
57
SHA-1 processes data by 512-bit blocks (64 bytes). For a given input message m, it first appends some bits (at least 65, at most 576) so that the total length is a multiple of 512. Let's call p the added bits (that's the padding). The padding bits depend only on the length of m (these bits include an encoding of that length, but they do not depend on the ...
27
RSA without padding is also called Textbook RSA.
The question why RSA without padding is insecure has already been answered
in this question.
We can fix a few issues by introducing padding.
Malleability: If we have a strict format for messages, i.e. that the first or last bytes contain a specific value, simply multiplying both message and ciphertext will ...
26
The key to understanding hash extension attacks is to understand that the hash output isn't just the output of the machine generating the hash, it's also the state of the machine up till that point. In other words, just the hash output alone contains enough information for you to keep going and append more content to the hashed input.
The catch is that ...
26
This describes some attacks against textbook RSA (also known as raw RSA), where the public or private functions $x\mapsto y=x^e\bmod N$ or $y\mapsto x=y^d\bmod N$ are applied directly to the message.
Encryption / Decryption
Determinism in textbook RSA allows an attacker - given a ciphertext - to search for the corresponding plaintext.
Determinism also ...
19
This is a common mistake, so I'd like to give an in-depth answer. Basically, what you are proposing is to rely on the ONE-WAYNESS of RSA as a ONE-WAY FUNCTION, rather than relying on its CPA or CCA security as an encryption scheme. The advantage of using RSA as a one-way function is that no padding etc is needed.
Now, the first important thing to note is ...
15
PKCS#1 v1.5 describes a method (formally known as RSAES-PKCS1-v1_5) that turns textbook RSA into a (heuristically) secure encryption scheme for small messages (PKCS#1 v1.5 also describes a signature scheme, which the question and this answer do not consider).
For a $k$-byte ($8k-7$ to $8k$-bit) public modulus part of public key $(N,e)$, the message to be ...
14
The algorithm you quote is usually called textbook RSA and is not used in practice for numerous security reasons (the problem you pointed out, is just one of them).
In practice, you have to pad (or armor) your message. This should be done using the RSA-OAEP (also called PKCS#1 v2.0) scheme. It transforms your message (1) into a pseudorandom block (not 1) ...
13
Well, the entire point of a cryptographical hash function is that no one can practically devise two messages that hash to the same value.
Now, the SHA family of hashes use the Merkle–Damgård construction; that is, they have an iterated hash function, and each invocation of the hash function takes as input a fixed block size (either 512 or 1024 bits in the ...
13
I recommend that you stick with the standard padding methods, even in your scenario.
Here's one reason, if your 'random password' consists only of the AES key, and you use the raw RSA operation on it (that is, zero pad it to the size of the RSA modulus, and then compute $M^e \bmod N$), then yes, there does exist weaknesses; there's a meet-in-the-middle ...
13
It is usually assumed that the length of the message is not secret. Even with padding the approximate length is leaked, and necessarily any encryption reveals a maximum length – or at least information content if compression is used – because the ciphertext cannot in general be shorter than the message.
NaCl's secretbox does not use a block cipher, but a ...
12
If you pad a 128-bit value $K$ with zeroes to the left, and interpret the value numerically with big-endian convention (as happens in PKCS#1 in general), you end up with a value which is no greater than $2^{128}$. If the public exponent is $e = 3$, then the "encrypted value" is no greater than $2^{768}$, and no actual modular reduction takes place. ...
12
How does the new attack work at top level?
In short
They used BEAST-like Man in the Browser attack by using Cache-like attacks to perform a downgrade attack against any TLS connection to a vulnerable server. With this, they showed the feasibility of using Cache-like attacks.
More detailed
Even over the years, numerous mitigation techniques are ...
11
Indeed, ISO 10126-1:1991 and ISO 10126-2:1991 titled Banking -- Procedures for message encipherment (wholesale) have been withdrawn circa 2007.
The padding specified by ISO 10126 was adding random until the message has length 7 (mod 8) bytes, then adding a byte coding the number of bytes added (including that byte), making the length 0 (mod 8) and suitable ...
11
Padding is always added, even if the plaintext is a product of the block size. This way the algorithm look for the last byte(s) and can safely interpret it as padding data. In case of alignment to the block size, a full block is added just for padding purposes.
So if your example shows 8 bytes of data and you are using a 64-bit block cipher, a block of ...
10
1. Why do we use padding?
Both block ciphers and RSA are permutations on a block(RSA's block isn't an integral number of bytes), so it's clear that both of them need some kind of padding if the data size doesn't correspond to the block size.
With block ciphers the padding doesn't do much: It fills up the remainder of the block, and tells you how much ...
10
TL;DR: Padding is part of the specification of the mode and thus doesn't need to be done by the user of the primitive.
Internally GCM really is CTR mode along with a polynomial hashing function applied on the ciphertext. CTR-mode doesn't need padding because you can just partly use the bits the last counter block generated and the polynomial hash does use (...
10
The Structure of PKCS#1 v1.5 as follows;
The message $m$ is padded to
x = 0x00 || 0x02 || r || 0x00 || m
and the ciphertext calculated as $c=x^e\bmod N$ not by $m^e\bmod N$, where $r$ is a random string.
Cube root attack cannot be applied since the padding guarantees that messages are not short.
The random $r$ make the encryption probabilistic so that ...
9
From what I understand, you consider a scenario in which a fixed, random-looking message $M$ is sent to multiple recipients, encrypted using RSA with some padding (this is called the "broadcast RSA" setting).
Moreover, you consider affine paddings, in the sense that you apply the RSA function to an element of $\mathbb{Z}_N$ of the form $a_i M + b_i$ for ...
9
SHA-1, SHA-224 and SHA-256 append the bit “1” to the end of the message, followed by k zero bits, where k is the smallest, non-negative solution to the equation l+1+k ≡ 448 mod 512, where l - message length. In second step they use 32-bit words.
SHA-384, SHA-512, SHA-512/224 and SHA-512/256 use different equation: l+1+k ≡ 896 mod 1024 and in 2. step ...
9
Textbook RSA encryption scheme is not IND-CPA secure as it is a deterministic scheme.
Textbook RSA signature scheme is not secure considering Existential Unforgability under Chosen Message Attack. e.g. if attacker $\mathcal{A}$ chooses random x $\in$ {1,2,...,n-1} and computes y = x$^{e}$ mod n, then sets m = y, $\sigma_{m}$ = x then $\sigma_{m}$ is a valid ...
9
One good reason not to use RSAES-OAEP for signature is because as it stands, it can't do signature! RSAES-OAEP performs encryption of a message (of limited length) with optional label into a cryptogram, and decryption thereof. There is no way to turn some RSAES-OAEP black box into a signing machine.
OK, we could define an RSA signature scheme with a ...
8
AES by definition takes 16, 24 or 32 bytes as key, and nothing else. If you have a different size input use some kind of KDF to transform it to the correct length.
If that input is a password this step is even more important. You should a key strengthening construction, such as PBKDF2 with sufficient iterations and a salt.
If you use authenticated ...
8
Is it somehow connected with sequentially reading in files /data of unknown length?
Yes, indeed. It is part of a requirement to perform online message processing, or, in other words, the ability to stream the data without knowing how much data to expect.
Would it make a difference if you always knew the length of the message to be hashed?
Well, yes, in ...
8
RSA PKCS#1 is still secure if padding oracles do not apply. If padding oracles apply, for instance when a server verifies the padding after decryption and somehow leaks the result (through an error message or by leaking information about the the verification time) then OAEP is much more secure.
Note that in principle OAEP can also leak information through ...
8
You are talking about the PKCS#7 padding. There is a simple reason; assume that when the last block is full and you don't apply the padding before encryption and then send the message.
When decrypting, the receiver needs to see a padding pattern to remove the padding. What if the last byte is 01 of the message? is it padding or the message itself? ...
7
Well, there are no necessary 'reduction in strength', for two reasons:
You ask about how many signatures you'd need to recover the private key. Well, even with unrestricted Oracle access to the private operation, there's no known way to recover the private key (or equivalently, factor the modulus) that's more efficient than just ignoring the Oracle and ...
7
I believe what you are seeing is that .NET automatically uses PKCS #7 padding. This will always add padding. Thus if your plaintext is a complete block length, one extra block of padding will be added.
The reason the ciphertext ends up being the same in both of your test cases is that it is adding the same padding in both cases (see PaddingMode Enumeration ...
7
The 16-byte IV and ciphertext (which together are part of the output of $e_m$) are assumed to be intercepted by an adversary. That reveals the number $b$ of 16-byte blocks in the ciphertext. With CBC and PKCS#7 padding, $b=\big\lceil{{n+1}\over16}\big\rceil$ where $n$ is the byte size of the plaintext (the file size). Putting $n$ itself in a header thus ...
7
In their 2012 paper "The Security of Ciphertext Stealing", Phillip Rogaway, Mark Wooding and Haibin Zhang prove that all the NIST-approved ciphertext stealing modes provide the same level of security as ordinary CBC mode, i.e. ciphertext indistinguishability under a chosen-plaintext attack. To quote their abstract:
"Abstract. We prove the security of CBC ...
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