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For example, in the Diffie–Hellman key exchange, an eavesdropper observes and exchanged as part of the protocol, and the two parties both compute the shared key . A fast means of solving the DHP would allow an eavesdropper to violate the privacy of the Diffie–Hellman key exchange and many of its variants, including ElGamal encryption .
The algorithm can be described as first performing a Diffie–Hellman key exchange to establish a shared secret , then using this as a one-time pad for encrypting the message. ElGamal encryption is performed in three phases: the key generation, the encryption, and the decryption.
The Diffie–Hellman key exchange method allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure channel. This key can then be used to encrypt subsequent communications using a symmetric-key cipher. Diffie–Hellman is used to secure a variety of Internet services. However ...
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
The baby-step giant-step algorithm could be used by an eavesdropper to derive the private key generated in the Diffie Hellman key exchange, when the modulus is a prime number that is not too large. If the modulus is not prime, the Pohlig–Hellman algorithm has a smaller algorithmic complexity, and potentially solves the same problem. [2]
A polynomial-time problem can be very difficult to solve in practice if the polynomial's degree or constants are large enough. In addition, information-theoretic security provides cryptographic methods that cannot be broken even with unlimited computing power. "A large-scale quantum computer would be able to efficiently solve NP-complete problems."
A format of one-time pad used by the U.S. National Security Agency, code named DIANA.The table on the right is an aid for converting between plaintext and ciphertext using the characters at left as the key.
The algorithm uses a key pair consisting of a public key and a private key. The private key is used to generate a digital signature for a message, and such a signature can be verified by using the signer's corresponding public key. The digital signature provides message authentication (the receiver can verify the origin of the message ...