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24

The SSL and TLS protocols (on which HTTPS is based) are designed in a way that no attacker (neither a passive nor an active one) can read anything of the encrypted part (if the cryptographic assumptions hold - and if you don't use the NONE cipher, which does no encryption). Of course, the attacker can read the negotiation part. But this part will not ...


23

ECDSA is a digital signature algorithm ECIES is an Integrated Encryption scheme ECDH is a key secure key exchange algorithm First you should understand the purpose of these algorithms. Digital signature algorithms are used to authenticate a digital content. A valid digital signature gives a recipient reason to believe that the message was created by a ...


20

The standard Diffie-Hellman key exchange algorithm (or family of algorithms) works in an cyclic group with generator $g$, and relies on $$ {y_A}^{x_B} = (g^{x_A})^{x_B} = (g^{x_B})^{x_A} = {y_B}^{x_A}, $$ where $y_A$ and $y_B$ are publicly transmitted, while $x_A$ and $x_B$ remain private. With three parties, we still have $$((g^{x_A})^{x_B})^{x_C} = ((...


19

The security of Diffie-Hellman depends upon the group in which DH is used, but not upon which generator is used for this group. See note 3.53 (chapter 3, page 103) of the Handbook of Applied Cryptography. In more details: for DH, we use a subgroup of size $q$ of the integers modulo $p$ (a big prime) with the multiplication as group operation. $q$ should be ...


19

Both RSA and Diffie-Hellman work with modular exponentiation. But they work in a different way: In RSA, there are two exponentiations which invert each other, i.e. we have $e$ and $d$ such that $(x^e)^d \equiv x$ for all $x$. E.g. if $\square^e$ is the encryption, $\square^d$ is the corresponding decryption. To create this pair of $e$ and $d$ (or derive one ...


18

The really great thing about Diffie-Hellman is how light it is, network-wise: both parties send each other a single message; neither has to wait for the message from the peer before beginning to computing his own message. If you can tolerate something heavier, you can have a look at what @Paŭlo describes; with $n$ participants, it requires $n-1$ messaging ...


15

I assume you're talking about SSL/TLS or a similar protocol. In these protocols there are two reasons to use Diffie-Hellman: Your certificate only supports signing Either it is an RSA certificate restricted to signing, or it uses an algorithm that doesn't support encryption, such as DSA or ECDSA. Forward security - What happens if the server's private key ...


15

What is usually meant by "group encryption" is not what you are after. Group encryption algorithms strive to achieve the following: a given message is encrypted, and may be decrypted only if sufficiently many group members collaborate. This is not what you seek; what you want is a system such that a given message can be encrypted once and every member of the ...


13

Say you encrypt a message with a key $k$. With symmetric encryption (ie. symmetric ciphers), $k$ must be secret. The sender and recipient must agree (somehow) on $k$. No-one else can be allowed to find out $k$. Anyone else who finds out $k$, can decrypt all the messages encrypted with $k$. For that reason, symmetric ciphers are often called "secret key" ...


13

Well, the advantages of static-ephemeral ECDH (and, they apply to DH as well): You get one-way authentication for free. That is, if Bob has Alice's public ECDH key, and uses it to talk to someone, Bob knows that that someone is Alice, without doing any further checks. Now, Alice has no idea who she's talking to; on the other hand, for some scenarios, ...


13

The first part of this partial self-answer uses additional information I received from Professor Simon R. Blackburn, one of the author of the recent attack. The method used to generate parameters is not public, e.g. for the matrix $m\in GL(n,\mathbb F)$ which careful choice was acknowledged critical to defeat an earlier version of the attack. The authors of ...


11

Most likely, this 'shared secret' was actually an IKE "preshared key"; it is used to authenticate the two sides (and, for IKEv1, is stirred into the keys). It actually isn't used as a key (and hence someone learning that key cannot use it to listen in, unless they perform an active Man-in-the-Middle attack). I suspect the password is the authentication ...


11

I recommend avoiding Diffie-Hellman parameter generation. Instead, use a standardized DH group with a sufficiently large modulus (2048-bit or larger). For example, group #14 or #15 from RFC3526 (see sections 3 and 4) would be a good choice. Alternatively, switch to the elliptic curve variant of Diffie-Hellman and use Curve25519. The article you linked to ...


10

You can do key agreement with asymmetric encryption. Any asymmetric encryption algorithm (post-quantum or not) can be used for key agreement: just choose a random key and encrypt it. Password Authenticated Key Exchange looks harder, because it cannot be applied on just any key exchange or asymmetric encryption scheme. The IPAKE framework can be applied on ...


10

Diffie-Hellman and RSA are distinct and do not use the same "trick". In Diffie-Hellman, commutativity is used: $(g^a)^b = (g^b)^a$. Both Alice and Bob do two modular exponentiations each (Alice chooses $a$, computes $g^a$ and sends it to Bob, receives $g^b$ from Bob, and finally computes $(g^b)^a$). Security relies on the difficulty of discrete logarithm: ...


8

The check $y_b^q = 1 \mod p$ is there to prevent two possible weaknesses: Suppose someone gave us (either because of a programmer error or deliberate attack) gave us a $y_b$ value of small order. If so, then someone listening in can guess the shared secret you derive. Suppose an attacker gave us a $y_b$ value with an order with a small factor $r$. Then, ...


8

Well, it depends on the which protocol is being used. For WEP and WPA, the keys used are derived directly from the pre-shared keys; that means that as long as you know the pre-shared keys, you can immediately decrypt packets as well. On the other hand, WPA2 is somewhat stronger; the two sides exchange nonces to derive the keys. Hence, unless you listen ...


8

An attack would be trivial if the seed of the RNG was only 32 bits; just enumerate the seeds, and test which matches the intercepted messages. That's easy. However the default Java Random class uses a 48-bit state and seed (which would still be attackable, though $2^{16}$ times less easily), and there are safe subclasses, thus use of Random does not imply ...


8

CRAM-MD5 is a protocol to demonstrate knowledge of a password. In the context of email, it is sometime used by an email client to authenticate to a POP, IMAP, or/and SMTP server. Basically, the password is used as the key of HMAC-MD5 in a challenge-response protocol. Among positive things there are to say about CRAM-MD5: The password is not exchanged in ...


8

You're describing a form of three-pass protocol, which is a communication mechanism where neither party needs to know each other's secret key. Wikipedia describes a helpful metaphor using a box that can be locked by two padlocks: First, Alice puts the secret message in a box, and locks the box using a padlock to which only she has a key. She then sends ...


8

Using lattices/ring-LWE, there is Lattice Cryptography for the Internet (by me), which inherits from Ring-LWE encryption, and has been implemented by Bos et al. with further improvements by Alkim et al. The underlying mechanism is conceptually DH-like, but uses completely different mathematics. We start with a uniformly random $a \in R_q = R/qR$, which can ...


8

What does DH add? Perfect Forward Secrecy. That is, suppose you have a secure session with the server Bob, and then you close the session down. Then, someone steals the server (or serves a warrant to the owner). If you use RSA to transport the random session key, well, the server still has the RSA private key, and so they'll be able to decrypt your ...


7

Well, what SSL uses to negotiate the symmetric keys depends on the ciphersuite that both sides agree upon. By far, the most common method is that the client picks a random value (the premaster secret), and encrypts it with the server's RSA public key. However, it is not that unusual for the ciphersuite to specify that the client and the server agree upon a ...


7

Fair exchange protocols aren't new by any means, but there is a lack of layman-friendly material out there, unfortunately. I think the high prevalence of theoretical cryptography in fair exchange protocols may be partially responsible for that. At any rate, here is the basic idea behind a fair exchange protocol. Suppose you have two parties, Alice and Bob, ...


7

There is nothing related to passwords in AES. AES uses 128-bit keys, i.e. sequences of 128 bits. How you come up with such a key is out of scope of AES. In some contexts, you want to generate these 128 bits in a deterministic way from a password (and possibly some publicly known contextual data, like a "salt"); this is a job for password hashing. In other ...


7

ElGamal appears to be used instead of Diffie-Hellman (or IES) in OpenPGP mostly because when that format was put together, there were some unresolved intellectual property issues surrounding both RSA and Diffie-Hellman, while ElGamal was unproblematic. This trend for ElGamal seems to stick around, mostly by force of habit, e.g. when switching to elliptic-...


7

It does not; the equation holds for any element $g$. The fact that $g$ is a generator means only that every element of the group can be obtained a key. This is not at all necessary for the protocol.


7

What's missing is the authentication of the entities. If you don't authenticate the entity then you don't know who you've established the master secret with. This means an attacker can pose as a man in the middle or the attacker can simply act as one of the entities. You can use static DH key pairs, but in that case the DH public keys must be trusted and ...


6

The mathematical problems behind DH and RSA are similar but not known to be directly related. It is still an open question if an oracle breaking DH can be used to construct another oracle that breaks RSA (or vice versa). It is mostly believed that the two problems are not reducible to each other in poly time. However, the complexity of the fastest known DH ...


6

Yes, it is. Because of the way public key crypto works, they wouldn't be able to decrypt it. First, realize that something encrypted with a public key can only be decrypted with the corresponding private key (or, depending on the algorithm, vice-versa). So lets say everyone (including the sniffer) has the server's public key. You encrypt something with it, ...



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