# All Questions

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### Why do all SSH-RSA Keys begin with “AAAAB3NzaC1yc”?

My Friend and I have been generating a few ssh2-rsa keys and noticed that all the public keys began with "AAAAB3NzaC1yc". The similarity extended to "AAAAB3NzaC1yc2EAAAABIwAAAQEA" between two keys I ...
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### Why RSA can't handle numbers above 76?

I'm going to encrypt the characters Zhu, and decrypt them using RSA. I'm using the public key $\{e, n\}$ and private key $\{d, n\}$. The values of $e$, $d$ and $p$ ...
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### Is 80 bits of key size considered safe against brute force attacks?

I came across KATAN Family of Ciphers for small domain input blocks . They cipher arbitrary block lengths 32,48,64 but their key size 80 bits only. Is 80 bits of key size considered safe with ...
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### What is the use of REAL random number generators in cryptography?

I understand the use of pseudo-random number generators. I am not getting mixed up between these and "real" random number generators. However, I don't understand for what a real random number ...
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### MIT says: mathematical theory behind encryption is wrong. What are the consequences?

A friend shared with me the following link: Encryption is less secure than we thought I'm not a security expert and could understand great part the article, except the section about noise, but what I ...
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### What is the difference between known-plaintext attack and chosen-plaintext attack?

I am very confused between the concept of known-plaintext attack and chosen-plaintext attack. It seems to me that these two are the same thing, but it definitely is not. Can anyone explain to me how ...
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### Are there practical upper limits of RSA key lengths?

Suppose one wanted to use RSA encryption for the sole purpose of sending key bits for use in symmetric crypto systems, a dedicated key exchange system so to speak. And say you didn't think that the ...
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### Can AES decryption be used as encryption?

Definition E: AES encryption D: AES decryption x: plain text y: encrypted text k: key In original AES cipher, encryption: y = E(x, k) decryption: x = D(y, k) Then I define the "reverse AES ...
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### Physical analogue for MACs

What would be a good analogue with which to describe Message Authentication Codes to a person who has little to no understanding of cryptography? For instance, a vault is a reasonable analogue for ...
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### Why would anyone use an elliptic curve with a cofactor > 1?

In cryptography, an elliptic curve is a group based on a finite field $GF(p^k)$; this group has $n$ elements on it, and we work on a prime-sized subgroup of size $q$. We denote the value $h = n/q$ as ...
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### How secure is AES-256?

The cipher AES-256 is used among other places in TSL/SSL across the Internet. It's considered among the top ciphers. In theory it's not crackable since the combinations of keys are massive. Although ...
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### How hard is to invert the function that computes the middle-bits of (x^2)?

I'm designing a function f that should be moderately hard to invert and very fast to evaluate in a modern CPU. The function will be used in a proof-of-work function. I've read that the middle-bits of ...
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### How does the MOV attack work?

What exactly is the MOV attack, how does it actually work, and what is it used for? It's explained briefly here and I'd like to know what it is more / what is it fully used for.
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### Can we ensure the security of a crypto-algorithm and -implementaton against acoustic cryptanalysis?

Like people always say: “Attacks only get worse…” — which is why I'm asking early. I have been reading the paper “RSA Key Extraction via Low-Bandwidth Acoustic Cryptanalysis” published December 18, ...
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### “Weaknesses” in SHA-256d?

According to this answer, "SHA-256d" was proposed in one of the Ferguson/Schneier books like so: SHA-256d(x) = SHA-256(SHA-256(x)) Apparently, the motivation for ...
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### Difference between Rijndael 128 / 256 blocksize implementations? (and impact of block size in general)

Can anyone shed some light onto the advantages/disadvantages of using Rijndael with 256-bit block size, as opposed to the 128-bit (AES) implementation? (please note: I'm not referring to key-size ...
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### Can CBC ciphertext be decrypted if the key is known, but the IV not?

Let's say that there is a binary file encrypted with AES in CBC mode (i.e. using a key and initialization vector). If key is known, but IV is not, is it easy to fully decrypt the file? How hard is ...
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### Can I select a large random prime using this procedure?

Say I want a random 1024-bit prime $p$. The obviously-correct way to do this is select a random 1024-bit number and test its primality with the usual well-known tests. But suppose instead that I do ...
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### UMAC: to what extent is it in use today?

Inspired slightly by the Encrypt-then-MAC question. The most obvious message authentication code is probably HMAC or RFC 2104 which is basically a hash of the input, an xor with a key... you get the ...
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### Is it possible to create an asymmetric cryptosystem where the private keys are not easily verifiable as such?

Plaintext that consists of an RSA key is easily recognizable as such, because it satisfies certain mathematical properties, in particular (See the answer for Why can an encrypted private key be brute ...
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### Is there an intuitive explanation as to why only the private key can decrypt a message encrypted with the public key?

I have just learned about using PGP/GPG for email encryption and one thing has always bugged me: How is it possible that a message encrypted with somebody's public key can be decrypted only with that ...
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### What to watch for with openssl generating weak keys? (low entropy)

(Disclaimer: I am regular software engineer with only basic crypto knowledge, so helpful if can be explained for a layman.) I am concerned about generating weak keys on a shared linux box with ...
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### Why is CAMELLIA suddenly so widely used?

When nowadays I point my browser to https sites, the cipher that is on most occasions used is Camellia. My browsers (Chrome and Firefox) seem to prefer it, even when AES is available. Is that not ...
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### What is difference between PRG, PRF, and PRP

Until what I have gotten is: A PRG is generator is a part of PRF that produces pseudo-random values for the function. PRF is semantically secure and has no worries of being invertible. Fine, then ...
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### How can I calculate the SHA-256 “midstate”?

Recently I've been trying to implement some Bitcoin-related code, and I've stumbled upon a weird concept, a SHA-256 "midstate". Some explanation is given here. The general concept is that Bitcoin ...
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### How can Cipher Block Chaining (CBC) in SSL be attacked?

I am trying to understand how CBC-mode in SSL/TLS can be attacked. I have been looking around online but all examples and explanations are very hard to understand and follow. Can you give a simple ...
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### Salting when encrypting?

I was attending a database encryption session at a developers conference. The presenter (who was a published author on the subject) said that MS SQL Server did not support salted hashes in the ...
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### Does chaining random number generators lead to loss of randomness?

Assume you chain random number generators, i.e use the result of one PRNG as the seed for the next. What kind of errors can that introduce in the randomness of the numbers generated?
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### Are any of the major asymmetric ciphers distinguishable (EG, RSA, ECC)?

Related to "Is it possible to derive the encryption method from encrypted text?". Given ciphertexts generated by any of the major asymmetric ciphers (RSA, ElGamal, ECC, etc..) can these ciphertexts ...
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### How broken is a xor of two LCGs?

Suppose we define a PRG as the xor of two LCGs modulo a 64-bit prime: something like the following Python code. ...
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### ElGamal with elliptic curves

I've searched some information on ECC, but so far I have only found Diffie-Hellman key-exchange implementations using ECC, but I don't want to exchange keys, I want to encrypt & decrypt data like ...
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### Why is there an enormous difference between SAT solvers?

SAT solvers are very important in algebraic attacks, for example walksat and minisat. However, when solving the benchmark problems available here there is an enormous performance difference between ...
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### repeating-key xor and hamming distance

I read that to break repeating-key xor you can do the following: try a keysize $n$ and compute the hamming distance between the first $n$ bits of the encrypted string and the bits $n+1$ to $2n$ of the ...
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### Why would you expect to find a collision in a hash function after approximately $\sqrt{n}$ hashes?

I can't get an intuitive understanding of why it's $2^{(\frac{n}{2})}$ and not $2^n$, where $n$ is the number of bits of which the key consists.
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### How does the index of coincidence work in the Kasiki test?

I'm starting to learn about cryptanalysis and I am having a bit of difficulty understanding the Kasiski test's index of coincidence. I have a book (Cryptography Theory And Practice by Douglas Stinson) ...
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### Attacks of the MAC construction $\mathcal{H}(m||k)$ for common hashes $\mathcal{H}$?

Consider a common practically-collision-resistant hash function $\mathcal{H}$ (e.g. SHA-1, SHA-256, SHA-512, RIPEMD-160), perhaps based on the Merkle–Damgård construction as are the first three. We ...
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### RIPEMD versus SHA-x, what are the main pros and cons?

RIPEMD is a family of cryptographic hash functions, meaning it competes for roughly the same uses as MD5, SHA-1 & SHA-256 do. The Wikipedia page for RIPEMD seems to have some nice things to say ...
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### Can one efficiently iterate valid bcrypt hash output values?

bcrypt is an intentionally slow hash algorithm. In my last protocol idea, I wanted to use it to expand a password and then only transfer the bcrypt-hashed password. An efficient attack on this would ...
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### Replacing the Rijndael S-Box?

The Rijndael S-Box design generates a permutation cycle of type $2+27+59+81+87$. What effect would replacing that permutation with a cycle of type $256$ have on the security of AES?
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I was trying to implement zero knowledge protocol for authentication based on the paper "A Practical Zero-Knowledge Protocol Fitted to Security Microprocessor Minimizing Both Transmission and Memory". ...
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### What is the origin of the word “Keccak”?

Where does the word or acronym Keccak come from? Guido Bertoni, Joan Daemen, Michael Peeters, and Gilles Van Assche. Keccak sponge function family main document. Submission to NIST (updated), 2009. ...
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### How to build an electro-mechanical public key cipher machine?

It is generally assumed that asymmetric encryption schemes were invented in 1973 at GCHQ in Britain and, independently, in 1976 at the MIT. Imagine, if the abstract idea of having a public key and a ...
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### Which blind signature schemes exist, and how do they compare?

I'm looking into blind signature schemes for use as digital cash. I have come across blinded RSA, and Lucre(DH based). Are there other schemes available, and how do they compare? I suspect there ...
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### What changed in PKCS#1 v2.2, and why?

PKCS#1 is one of the most used (de-facto) standard for real-world use of RSA. That's for good reasons: PKCS#1 is well thought, versatile, understandable, has been relatively stable for over two ...
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### How to break an arbitrary XOR and Rotation based encryption?

I heard encryption based purely on XOR and Rotation is inherently weak. The paper Rotational Cryptanalysis of ARX says: It is also easy to prove that omitting addition or rotation is devastating, ...
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### Why is the salt used only once in PBKDF2, while the password is used often?

The purpose of PBKDF2 is to create a derived key (DK) from a master password (PW) and a salt, often using a function like HMAC-SHA256. I have read that the salt should be as random as possible. But ...
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### Hash function from narrower block cipher operated in CBC-encryption mode?

I am trying to build a public hash function (thus collision-resistant and preimage-resistant, and more generally behaving like a random oracle), with input a message $M$ of fixed size $|M|=m\cdot b$ ...
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### GPG/PGP Verification of Revocation

How does one verify a key revocation? After revoking a key and sending the revocation to MIT's keyserver, I noticed that the key is listed as such: ...