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69

A random oracle is described by the following model: There is a black box. In the box lives a gnome, with a big book and some dice. We can input some data into the box (an arbitrary sequence of bits). Given some input that he did not see beforehand, the gnome uses his dice to generate a new output, uniformly and randomly, in some conventional space (the ...


44

There are a variety of reasons why AES is more widely used: AES is a standard. AES has been vetted by cryptanalysts more extensively than Camellia. As a result, we can have greater confidence in the security of AES than in Camellia. Therefore, on the merits, there may be good reasons to choose AES over Camellia. AES is a government standard (FIPS). ...


28

As a bonus feature, AES has hardware support in Intel processors which implement the AES instruction set, with AMD support coming soon in their Bulldozer based processors. The AES instructions set consists of six instructions. Four instructions, namely AESENC, AESENCLAST, AESDEC, AESDECLAST, are provided for data encryption and decryption (the ...


22

Actually the article you link to does not say that a balanced Feistel cipher is less secure than an unbalanced one; it says that the security of an unbalanced Feistel cipher is more easily proven, given enough rounds. Luby and Rackoff have shown in 1988 that a balanced Feistel scheme with only 4 rounds is "perfectly" secure as long as the round functions ...


18

You don't want to use something like the Mersenne Twister for gambling. It is not cryptographically secure. Given a small amount of output, it is relatively straightforward to compute all future outputs. These algorithms are designed for things like Monte-Carlo simulations and things of that ilk. A better option is to select a 128-bit key at random and ...


15

Disclaimer: I use Coq on daily basis... I have seen in some places that people use formal verification and/or computer-aided verification for cryptography. To my knowledge, there aren't that many places that do such a thing. :) First lets make sure we talk about the same concepts: Formal Verification: The act of proving the correctness of ...


13

Using the book as a key is relatively similar to one-time pad, insofar as the book can be considered as a random stream of characters. But that's true only to some extent: a book consists of words, with meaning, which implies that characters which may appear at position 321:42:35 are not uncorrelated with characters which appear at positions 321:42:34 and ...


13

Your second question was about programmability. This hasn't been directly addressed yet by Thomas' answer or the comments, so I'll focus on that question only. Unfortunately I don't know of a simple primitive that is secure in the random oracle model that requires programmability, but I'll use one that is hopefully clear once I explain the background. It's ...


13

In theory. No. The inverse of a secure PRP need not be a secure PRP. Here is what we can guarantee. The inverse of a secure sPRP (strong-pseudo random permutation) is guaranteed to be a secure sPRP. Any secure sPRP is a secure PRP. Therefore, the inverse of a secure sPRP will be a secure PRP. FYI, if you are not familiar with PRP/sPRP, the difference ...


12

A random oracle is an ideal object; see this previous question for some details. What makes a random oracle convenient for proofs is the part about knowing nothing on the output for a given input if you do not try it. For instance, consider the following encryption scheme: $H$ is a random oracle which outputs $n$-bit values. The key is a $K$, a string of $...


11

There are a couple of options for protocol analysis tools. (I don't know any established tool for their design - as said by someone else, designing your own protocols is not really recommended.) If you are looking for formal methods based, symbolic tools, some well-known tools that have been applied to many protocols are ProVerif and Scyther. Given that you ...


10

Not all ciphers can be broken, even by infinitely powerful adversaries. When used correctly, the One Time Pad (OTP) is information-theoretic secure, which means it can't be broken with cryptanalysis. However, part of being provably secure is that you need at least as much key material as you have plaintext to encrypt. Such a key needs to be shared between ...


10

There is no direct inference from $P = NP$ or $P \neq NP$ to security or insecurity of any particular encryption algorithm. As far as practical consequences are concerned, the "$P = NP$" problem is severely overhyped. If $P = NP$ then any problem for which a solution can be verified in polynomial time can also be solved in polynomial time. "Polynomial time" ...


10

The usual approach to prove IND-CPA security is to construct a logical argumentation called "reduction". In this argumentation you first start with the assumption that certain computational problem is hard (for example, the Decisional Diffie-Hellman assumption), and then you proceed to demonstrate that if your crypto scheme were insecure with respect to IND-...


9

I hope I got your point and try to answer your question. Actually, if I understand you right, then what you call an attack actually means an adversary acting in a specific attack model. To clarify this, we need to review the security models for digital signature schemes and when we have discussed this we can clarify issues. Basically, we have to discuss ...


9

A fast 64-bit hash cannot be completely secure, since a $2^{32}$ brute force collision search is completely doable, and even a $2^{64}$ preimage attack could be feasible. As a MAC used for hash table keying, that doesn't really matter (unless you leak the key). Finding just a few collisions isn't a problem and gathering statistics for an attack would ...


9

The ideal encryption scheme $E$ would be one that, for every ciphertext $C=E(K, M)$, if the key remains secret for the adversary, the probability of identifying $M$ is negligible. Since that is not possible in practice, the second most reasonable approach is to define constraints strong enough to satisfy some definition of security. The $IND-$ notation ...


9

This is very confusing because it seems as it should be something really easy to prove. However, it actually is not, and in fact the proof uses the Borel-Cantelli lemma. Anyway, it was formally proven by Rudich and Impagliazzo in their groundbreaking work on black-box separations. You can find a formal proof in Rudich's thesis, Section 6.2, or in the paper ...


8

Summary. This scheme is insecure. It can be cryptanalyzed using standard methods from the cryptanalytic literature. It also has poor performance. Your algorithm. To summarize your scheme, in your algorithm a one-bit message $m \in GF(2)$ is encrypted by picking a random quadratic polynomial $p(x_1,\dots,x_{128})$ in $GF(2)[x_1,\dots,x_{128}]$, setting $c =...


8

When cryptographers create algorithms, they usually provide some argument that the algorithm is secure. They need to start the argument with some set of assumptions. For example, the in public-key cryptography, they may begin with the assumption that factoring large numbers is hard. Many algorithms use use a block cipher as a building block. The arguments ...


8

An Ideal Cipher with $k$-bit keys and a $b$-bit blocksize is a family of $2^k$ permutations on the set $\{0,1\}^b$ indexed by the set $\{0,1\}^k$, selected uniformly at random from the set of all such families of permutations. See e.g. http://eprint.iacr.org/2005/210.pdf. The IC model is primarily useful for proofs where you need to assume that the ...


8

That sounds like an overly succinct description of the 'Find then Guess' (FTG) notion of security, described in the paper "A Concrete Security Treatment of Symmetric Enryption". And you are correct, there is something the test is missing: the two 'challenge' plaintexts must be the same length ($|m_0| = |m_1|$). Also, the description is so succinct I can't ...


8

The generic model for a MAC is the following: the attacker is given access to a block box which implements the $S$ function with a key $k$ that the attacker does not know of. The attacker is allowed to make $q$ requests to the box on messages that he can choose arbitrarily. The goal of the attacker is to make a forgery, i.e. produce values $m$ and $t$ such ...


8

Computationally indistinguishable typically means that your adversary is computationally bounded and that because of this they cannot distingush between, for example, two messages. For example, say you encrypt (with proper padding) the messages $0$ and $1$ using RSA and send them to the adversary. We would not want the adversary to be able to distinguish ...


8

One line: worst means any and average means random. Lattice-based cryptosystem Let me restate. Fix security parameter $n$. What the reduction shows is the existence of a solver for the lattice problem on input any $n$-dimensional lattice using the adversary breaking a lattice-based cryptosystem with the security parameter $n$ on the average case. Since ...


8

Reductionist security In a reductionist security proof for some cryptographic protocol $\Pi$ to some alleged hard problem $P$ means, that we can build an algorithm $\cal B$ for solving $P$ if we have access to a hypothetical algorithm $\cal A$ that efficiently breaks the security definition for the protocol $\Pi$. In general, showing a polynomial time ...


8

Your problem seems to be at least as hard as the 2-weak Bilinear Diffie-Hellman Inversion Problem (2-wBDHI problem): Given $g, g^x, g^{x^2}, g^y \in \mathbb G$, and $T \in \mathbb G_T$ to determine whether or not $T = e(g,g)^{x^3 y}$. Proof: We first need to define an equivalent version of your problem, where we take some generator $h$ so $g = h^b$. ...


8

You can generate a random string $s_1$ as long as the plaintext. Then XOR this value with the plaintext generating $s_2$. Now encrypt both parts using $\mathrm{Enc}_1$ and $\mathrm{Enc}_2$. You need to decrypt both to XOR the two parts together again. This is similar to secret sharing where you need two parts of a key to decrypt. If $\mathrm{Gen}_1$ and $\...


8

Just looking for a Turing machine vs circuit is a bit misleading. The important distinction is uniform (complexity class BPP) vs non-uniform (complexity class P/poly) adversaries. You can characterize P/poly in terms of circuit families, but also in terms of Turing machines with arbitrary "advice strings." In fact, the latter is the more traditional ...


7

In step 2, the adversary outputs two messages. One of these will be selected at random for encryption. You can think of the adversary sending these messages to a "challenger" that also has oracle access (or is the oracle itself). It doesn't really matter who is running the challenge since the challenger doesn't have any "intelligence." All the challenger ...



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