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14

These are completely different things: Man-in-the-middle is an active attack to a cryptographic protocol, where the attacker is, effectively, in between the communications of two users, and is capable of intercepting, relying, and (possibly) altering messages. In this case, the meaning of "in the middle" is direct: the attacker is in the middle of two ...


9

How could this allow for a backdoor? Well, if you do DH modulo a composite, an attacker can recover the shared secret if they can solve the DH problem (or the DLog problem) modulo each of the primes that make up the composite. There are a couple of ways that could be used by someone who knows the factorization to solve the DLog problem easier than ...


5

Ephemerality does not refer to "a new session key being made each time a new session is set up", it refers to both parties' key pairs (and group elements) being freshly chosen. ‚ÄčThese Diffie-Hellman key pairs are should be ephemeral for forward secrecy; the session key is always ephemeral, even if static-static Diffie-Hellman is applied. Any nonces are used ...


2

You need an authentic channel from Alice to Bob to get a secret channel from Bob to Alice. This assumption is missing in a), so anyone in control of the communication channel can play man in the middle on any protocol. As long you don't have a secret channel from Alice to Bob or an authentic channel from Bob to Alice, Alice will never (= for any protocol) ...


2

I will assume for simplicity that you're talking about the full multiplicative group of $F_p$ instead of a proper subgroup, thus there are no problems with $g^a+1$ (except when $g^a=p-1$ which can be trivially ruled out by comparing to $p$). The quantity $\log_g(g^a+1)$ is sometimes referred to as the Zech logarithm (strictly speaking, it is defined for ...


1

You can use ephemeral Diffie-Hellman and then use RSA to authenticate the parameters and established key seed the same way as TLS does. Java Card implementations usually contain an implementation of ECDH key agreement. An advantage is that you don't need very large key sizes to be reasonably secure. Furhtermore, ECDH operation and key pair generation is ...


1

Both RSA and DH have a similarity which is the Modulus Exponential (modexp) function (RSA encrypt/decrypt function). Since both RSA and DH uses the same modexp function, you can make full use of the Cipher for ALG_RSA_NOPAD in JavaCard's crypto API. I have sat down and taken time to adapt the RSA crypto functions for traditional non-ECC type of DH functions ...


1

Diffie-Hellman relies on a mathematical problem on positive integers. To use it with bytes you just have to convert the bytes to - or use the bytes as - an integer. Usually this would be a unsigned big-endian (or network order) integer. For Diffie-Hellman the parameters consist of the modulus and the base. The public value could be 1024 bits (128 bytes). ...


1

There is 3 kind of discrete log problem as you explained : Diffie-Hellman problem (Dlog): Pick $a \in \{1,\ldots,q\}$. Compute $A = g^a (mod\ p)$ Given $(p,q,g,A)$ find $a$. Assumed hard. Computational Diffie-Hellman problem (CDH) : Pick $a,b \in \{1,\ldots,q\}$. Compute $A = g^a (mod\ p)$ and $B = g^b (mod\ p)$ Given $(p,q,g,A,B)$ find $g^{ab}$. Note ...


1

Simply put, there are two key-pairs for DHE_RSA instead one key-pair of RSA_RSA. For example, for AES128_CBC_SHA(long name is RSA_RSA_AES128_CBC_SHA), you have one key-pair for both key-exchange and authentication. for ECDHE_RSA_AES_CBC_SHA, you have two key-pairs. The ECC key-pair is temporary for key-exchange. The RSA key-pair from cert is used for ...


1

Using ECDHE as an example, the steps are like this, The client sends supported named curved list. The server chooses a curve and generate key-pair, and sent back curve type and public key. The client uses the server curve type to generate key-pair, and send back curve type and public key. Now, both client and server can generate same secret(i.e. ...



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