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19

Modern security has moved beyond looking just at passive attacks (in which the attacker is just a passive eavesdropper seeking to learn what was said); attackers are generally considered to be able and willing to pull off active attacks of various types (in which the attacker can modify or forge messages to achieve some goal). One-time pads are extremely ...

12

Synchronous stream cipher, or just stream cipher. In a synchronous stream cipher a stream of pseudo-random digits is generated independently of the plaintext and ciphertext messages, and then combined with the plaintext (to encrypt) or the ciphertext (to decrypt). In the most common form, binary digits are used (bits), and the keystream is combined with ...

9

No, you can reuse a message as often as you want with the OTP. (But never reuse the key!) What happens if you reuse a key? The attacker can xor the two encrypted messages (ciphertexts) and gets the xor of the two plaintexts. The xor of two messages is highly insecure and can be easily turned into two plaintexts with some know patterns. What happens if you ...

5

First of all there does exist information theoretically secure message authentication codes suitable for use with a one time pad. An HMAC is not one of those information theoretically secure. As far as I recall the first article presenting such a construction is the 1981 article by Wegman and Carter: New hash functions and their use in authentication and ...

5

This is not a mathematical proof. A notable place it fails to be a proof is here: Pay attention to which cipher text I use, look up to match the message with the cipher-number below. $$cipher1⊕cipher3=character1⊕character3⊕IV1⊕IV2$$ (Note that the cipher BOTH use the SAME KEY, but they remain secure because of the two different IV) This line is ...

5

At least, doing the goof of reusing the OTP makes one vulnerable to disclosure of any of the key, which trivially reveals all the others. For the rest, the consequences depends heavilly on what the keys are intended for. If the keys are intended for a block cipher that is secure including under related-key attack (as AES almost is), then there is not ...

4

Since bits are independently generated, the entropy of the key is the sum over the entropy of the individual bits. The following calculations use the chance $P(x)$ of a zero or one bit. The first 5 bits are constant and thus have 0 entropy. The others are unbiased and have 1 bit of entropy each. $P(0)=P(1)=0.5$. $-2\cdot(0.5 \cdot \log_2(0.5))= ... 4 A one time pad (OTP) should by definition not have any patterns. An entropy source can have patterns, but an OTP by definition should consist of pure random bits. In general you can create something that is close to a true random number generator by applying a cryptographic hash function over the output of an entropy source. According to NIST you should ... 4 Not as secure as a one time pad. A key concept with one time pads is that no part of them is ever reused. It is a common pitfall of people attempting to implement cryptography to assume that an obscure relationship is necessarily a secure one: it is not. You are create a chain of SHA hashes that can be observed, and potentially decoded. Therefore what you ... 4 The system described in the quoted article depends on the security of AES for random keys (not only on the theoretical unbreakability of the OTP) in at least at least two things: the encryption of large files, as apparent in the quotes of the question; the initial establishment of the OTP, as shown by this other quote The first step is always optical, ... 4 If you perform the distribution digitally (using networks) then you have a problem. Unless you use another one time pad you lose the perfect confidentiality as the distribution itself won't deliver perfect security. But using another one time pad is pointless: you would lose exactly as many key bits as you are distributing, while you are only protecting the ... 4 fkraiem's answer is correct, but more context is required, in my opinion. The one-time pad (the theoretical device) has not been broken. But real-world systems based on the one-time pad have failed in practice. Systems based on one-time pads have failed in the past because key material has been reused, either by mistake or because the sender had ran out of ... 4 In a lot of cases OTP will be completely impractical. If instead of a truly random pad you use a pseudo random pad, you will have something a lot more practical. But it is no longer OTP, and the security proofs about OTP means nothing in that case. I think this is the essence of the Bruce Schneier quote you mention. If we for a moment ignore the impractical ... 4 I believe you need a few clarifications to answer this question yourself. The first is the one time pad (OTP). This is the only truly unbreakable system if it's used correctly. Using correctly means that for every symbol of the message there is exactly one truly random symbol in the key. Specifically, this means that there is no chosen symbol of the key ... 4 This cipher is called a one-time pad. It is unbreakable ("perfect secrecy") assuming that: The pad (the collection of random bits) really is truly random The pad is never reused to encrypt other messages So, no information can be extracted from$\text{file} \oplus \text{random bits}$. The basic idea of the proof is that an attacker can test every ... 3 Simply put: No. First recall that this is a mis-use of the term "One Time Pad" So lets call it a Vigenère cipher instead. You can determine this is insecure with a simple algebraic combination:$ \text{attack} = cipher_1 + cipher_2 + cipher_3 + cipher_4 \\ \text{Simplify: } \\ \text{attack} = character_1 + key_1 + IV_1 + character_2 + key_2 + IV_1 + ...

3

No, because then you could calculate $z_1 \oplus z_2 = (m_1 \land m_2) \oplus (m_1 \lor m_2) = m_1 \oplus m_2$. In practice, you can only find $m_1 \oplus m_2$ if both $m_1$ and $m_2$ are encrypted with the same OTP (i.e., $(m_1 \oplus y_1) \oplus (m_2 \oplus y_1) = m_1 \oplus m_2$). So without any knowledge of $m_1$, $m_2$, $y_1$ or $y_2$, there is no way ...

3

It depends on what you think of as an alternative. If you think of the scheme where you do not use $M$ as a modulus, but the keys a picked as: $$k \leftarrow \{1, \ldots, M-1\}$$ Encryption: $$C = d + k$$ Decryption: $$d = C - k$$ Then the scheme is insecure. One way to see this is to note that we have $C \geq d$. So the ciphertext communicates the ...

3

For a scheme to be information-theoretically secure, you need that $$\Pr[M=m\mid C=c]=\Pr[M=m\mid C=c^\prime]$$ for all $c,c^\prime$ (that is, any ciphertext has the same probability $M=m$, so the ciphertext doesn't change the probability $M=m$). Let's suppose we have a $c$ and a $c^\prime$. Both of them have the same number of ones and zeroes, because both ...

3

Note: In this answer, I stick to a definition of the One Time Pad where the random pad is used only One Time; at least, I've the name of it as support! Otherwise, it is well known that the OTP encryption scheme consisting of XOR with a repeated key is insecure by even the weakest standard (unknown plaintext with redundancy). INDistinguishability under ...

3

No, it's not secure; after three messages, the attacker can gain information about the second and third messages. To review this in greater detail, lets look at your proposal, and what it actually exposes to the user: To start with, you have a secret $x_0$ and $y_0$ (I'll subscript them to distinguish the values between the iterations). To encrypt the ...

2

For the one time pad, your key must be The same length as the message. Whatever your unit of measurement (bits, bytes, etc), they must be the same length. The key must be perfectly random. The key is only ever used once.

2

No. As the key should be fully random - a premise that invalidates the use of an OTP in practice - that should not matter at all.

2

The standard random number generator, in languages like Java or Python, does not generate real random numbers but pseudorandom numbers determined by an initial seed value. If an attacker can somehow guess or determine this seed value, they can reconstruct the entire sequence of pseudorandom outputs. Furthermore, the default pseudorandom number generators ...

2

The proof for the perfect secrecy property of the one time pad is quite simple. It makes use of basic probabilities and it says that: $$Pr[M=m|C=c]=Pr[M=m]$$ for a probability distribution M$\{0,1\}^n$ for the message space and a probability space C for the ciphertext space. Proof: Pr[C=c]=\sum{Pr[C=c|M=m']\cdot Pr[M=m']} =\sum{Pr[K=m'\oplus c]}\cdot ...

2

Could someone even recognize that the values are encrypted? Well, maybe, maybe not. You're correct that the values would all appear to be valid dates (this is known as format-preserving encryption, by the way), so they would not look obviously encrypted, the way, say, a random hex string would. If someone just saw a small number of such dates, with no ...

2

Yes, the same weaknesses apply. Text on computers is a bunch of numbers; a OTP encrypts a sequence of numbers modulo 2.

2

Imagine that you have a ciphertext: Perfect secrecy means, that without knowing the key, any plaintext has to be a possible preimage. Because otherwise the ciphertext would give you information about the plaintext. Encryption is an injective function, because otherwise it could not be reversed. That means, for a given key and ciphertext you have at most ...

2

Actually, it's not a hare-brained idea at all; you certainly can do integrity checking using a one-time pad. However, I believe that you'll need to use the one-time pad bits a bit faster than you'd expect, to achieve a forgery probability of at most $2^{-32}$, I believe you'll need at least 64 pad bits per packet (assuming informational theoretical security ...

2

First, the system as I understand it does not use a one-time-pad at all, but a steam cipher. The keystream is generated via a CSPRNG, and is not truly random, so it cannot be a one-time-pad. They are misrepresenting it. But, to answer your question, let's assume the system did in fact use a one-time-pad, and used it in the manner described. In this ...

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