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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

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

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 ...


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 ...


3

The security notion one usually considers for OTP is perfect secrecy, which informally means that the ciphertext does not reveal any information about the original message, regardless of the computational power of the adversary. It is already known that this requires that the key size must be equal to the plaintext size and that all keys are equiprobable. ...


3

This scheme follows the KEM/DEM approach of contructing secure asymmetric encryption schemes. However for a KEM/DEM PKCS (public key cryptosystem) to be secure it is required that both the key encapsulation mechanism (KEM) and the data encapsulation mechanism (DEM) are CPA or CCA secure for CPA or CCA of the whole scheme. Indeed the DEM looks CPA secure as ...


3

Sorry, I would only give partial points for a CCA attack on this scheme. The answer by @SEJPM is of course correct (and very informational so it's good it was posted). However, it is not the "best" answer, since this scheme can be easily broken under a chosen-plaintext attack. I will not write the full answer out (so that I can leave some work to be done for ...


3

No, that doesn't work. OTP is secure because knowledge of the plaintext doesn't give you any useful information about the key. This is because the bits of the key (e.g. $P_0$) are never used to encrypt anything else. If you would somehow reuse the key then leakage of the plaintext would cause leakage of $P_0$. Leakage of $P_0$ directly leaks $P_1$. I.e. ...


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

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.



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