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Public-Key Encryption
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
8.23 Note (security of ElGamal encryption) The problem of breaking the ElGamal encryption scheme, i.e., recovering m given p, α, αa, γ, and δ, is equivalent to solving the Diffie-Hellman problem (see §3.7). In fact, the ElGamal encryption scheme can be viewed as simply comprising a Diffie-Hellman key exchange to determine a session key αak, and then encrypting the message by multiplication with that session key. For this reason, the security of the El-Gamal encryption scheme is said to be based on the discrete logarithm problem in ℤp*, although such an equivalence has not been proven.It is critical that different random integers k be used to encrypt different messages. Suppose the same k is used to encrypt two messages m1 and m2 and the resulting ciphertext pairs are (γ1, δl) and (γ2, γ2).Then γl/γ2 = m1/m2,and m2 could be easily computed if m1 were known.
Cryptographic Approaches to RFID Security and Privacy
Published in Syed Ahson, Mohammad Ilyas, RFID Handbook, 2017
Koutarou Suzuki, Miyako Ohkubo, Shingo Kinoshita
Juels and Pappu [22] propose an encrypted ID scheme employing the ElGamal encryption and re-encryption technique. ElGamal encryption is a public key encryption with secret key x, public key (g, y = gx), and ciphertext E(m,r) = (gr, myr), where m is the message and r is a random value. It can be randomized by multiplying (gr × gs, myr × ys) using only a public key (g, y); this is called re-encryption. In the scheme, the ElGamal encryption of ID E(ID, r), is stored in the tag. The reader can update the ElGamal encryption of ID E(ID, r) by randomizing it without decryption and secret key x. Thus, readers are not required to have a secret key.
Blockchain Architecture, Components and Considerations
Published in Shaun Aghili, The Auditor's Guide to Blockchain Technology, 2023
Aafreen Fathima Altaf Hussain, Temitope Ipentan, Mahakpreet Singh, Grace Moyo Adeyemi
Elgamal encryption was developed by Taher Elgamal in 1984. The asymmetric key encryption was established based on the Diffie-Hellman key exchange principle. Distinct from the Diffie-Hellman algorithm, the Elgamal cryptosystem is a complete encryption and decryption system that depends on the discrete logarithm problem. The Elgamal algorithm consists of three components which are the key generator, the encryption and the decryption [58].
ElGamal-type encryption for optimal dynamic quantizer in encrypted control systems
Published in SICE Journal of Control, Measurement, and System Integration, 2021
Kaoru Teranishi, Kiminao Kogiso
ElGamal encryption is a tuple , where is a key generation algorithm, is an encryption algorithm, is a decryption algorithm, is a public key, is a secret key, q is a k bit prime, p = 2q + 1 is a safe prime, g is a generator of a cyclic group such that , , , and r and s are random numbers in . and perform elementwise operations for a vector and a matrix.