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Actually, there is one potential problem to reusing $a$ values: Background: $g$ generates a subgroup of size $q$; $q$ is a divisor of $p-1$, but it is usually selected as a prime, and is hence less than $p-1$ (which is obviously composite). What an attacker could do is, for any small prime $r$ which divides $(p-1)/q$, he can potentially learn $a \bmod q$; ...


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In the seminal paper of Diffie-Hellman describes Diffie-Hellman Key Exchange* (DHKE), we have Alice and Bob want to key exchange and Oscar is the bad guy (Oscar is not mentioned in the paper). In DHKE settings $p$ is a public prime modulus known by Alice and Bob and Oscar. $g$ is a public base known by Alice and Bob and Oscar and need not to be a prime ...


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I give a python program to clarify the above answer. Given the Elliptic curve $E:y^2= x^3+2 x + 2 \pmod {17} , \#E=19$ and a primitive point $P=(x_p,y_p)=(5,1)$ on the curve. We calculate the $nP$ # -*- coding:UTF-8 # Extended Euclidean algorithm def extended_gcd(aa, bb): lastremainder, remainder = abs(aa), abs(bb) x, lastx, y, lasty = 0, 1, 1, 0 ...


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How DH Key Exchange works: Server sends group parameters i.e. g which is generator and a large prime p.Server choose a random a and calculate g^a mod p. This value is signed with the private key from the server's certificate, an MiTM cannot change this value. Also Discrete logarithm Problem states that give above value and g and p, it is tough to a. These ...


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During 90's , US government had strict regulation that any software exported outside can have maximum 512 bits of RSA/DH , 40 bits of RC2/RC4 etc. These are called as export grade cipher and example of cipher suite is TLS_DH_anon_EXPORT_WITH_RC4_40_MD5 which means 512 bits of DH keys and 40 bits of RC4 for symmetric encryption. So for example, Netscape ...


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1. Before Bob computes $S_B(\mathit{B_K, A_K})$ does he hash $B_K$ and $A_K$ using $SHA256$ for example so Alice can hash them herself and compare the hashes? Generally the signature generation function already includes a hash operation (which might be SHA-256) so requiring a separate hashing step isn't required; it should be configured for the ...


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GCM is an authenticated encryption scheme; it allows Alice and Bob to detect if messages have been tampered. If the DH exchange is authenticated, then you don't need to sign anything.


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