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Topic: ElGamal encryption

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ElGamal

Generating set of a group

Taher ElGamal

	ElGamal encryption - Wikipedia, the free encyclopedia
		ElGamal consists of three components: the key generator, the encryption algorithm, and the decryption algorithm.
		ElGamal is a simple example of a semantically secure asymmetric key encryption algorithm (under reasonable assumptions).
		Encryption under ElGamal requires two exponentiations; however, these exponentiations are independent of the message and can be computed ahead of time if need be.
	en.wikipedia.org /wiki/ElGamal (771 words)

	ElGamal signature scheme - Wikipedia, the free encyclopedia
		The ElGamal Signature scheme is a digital signature scheme which is based on the difficulty of computing discrete logarithms.
		The ElGamal signature algorithm described in this article is rarely used in practice.
		The ElGamal signature scheme must not be confused with the ElGamal encryption which was also invented by Taher ElGamal.
	en.wikipedia.org /wiki/ElGamal_signature_scheme (394 words)

	ElGamal encryption: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-11-02)
		An asymmetric key encryption algorithm is considered semantically secure if it is not possible for a computationally-bounded adversary to derive significant...
		Probabilistic encryption is the use of randomness in an encryption algorithm, so that when encrypting the same message several times it will, in general, yield...
		A chosen ciphertext attack is an attack on a cryptosystem in which the cryptanalyst chooses ciphertext and causes it to be decrypted with an unknown key....
	www.absoluteastronomy.com /encyclopedia/e/el/elgamal_encryption1.htm (1807 words)

	Encryption Laws (Site not responding. Last check: 2007-11-02)
		In the mid-1970s, strong encryption emerged from the sole preserve of secretive government agencies into the public domain, and is now employed in protecting widely-used systems, such as Internet e-commerce, mobile telephone networks and bank automatic teller machines.
		Encryption can be used to ensure secr, but other techniques are still needed to make communications secure, particularly to verify the integrity and authenticity of a message; for example, a message authentication code (MAC) or digital signatures.
		Encryption can be done in several ways, only one of which uses a cypher.
	www.wwwtln.com /finance/69/encryption-laws.html (926 words)

	ElGamal discrete log cryptosystem - TheBestLinks.com - Group (mathematics), NSA, Pretty Good Privacy, Private key, ... (Site not responding. Last check: 2007-11-02)
		ElGamal is a simple example of a semantically secure asymmetric key encryption algorithm.
		It is probabilistic, meaning that a single plaintext can be encrypted to many possible ciphertexts, with the consequence that a general ElGamal encryption produces a 2:1 expansion from plaintext to ciphertext.
		Breaking ElGamal is, in most cases, at least as hard as solving the discrete logarithm problem.
	www.thebestlinks.com /ElGamal.html (379 words)

	Python Cryptography Toolkit
		For a secure encryption algorithm, it should be very difficult to determine the original plaintext without knowing the key; usually, no clever attacks on the algorithm are known, so the only way of breaking the algorithm is to try all possible keys.
		This poses a problem: you may want encryption to communicate sensitive data over an insecure channel, but how can you tell your correspondent what the key is? You can't just e-mail it to her because the channel is insecure.
		Encryption does not require the private key to be present inside the key object.
	www.amk.ca /python/writing/pycrypt (7734 words)

	The ElGamal public key system (in Technology > Encryption @ iusmentis.com)
		Although the inventor, Taher Elgamal, did not apply for a patent on his invention, the owners of the Diffie-Hellman patent (US patent 4,200,770) felt this system was covered by their patent.
		Elgamal's last name does not have a capital letter 'G'.
		A disadvantage of the ElGamal system is that the encrypted message becomes very big, about twice the size of the original message m.
	www.iusmentis.com /technology/encryption/elgamal (246 words)

	ElGamal encryption - (Site not responding. Last check: 2007-11-02)
		ElGamal can be defined over any cyclic group $G$ .
		ElGamal's security rests, in part, on the difficulty of solving the discrete logarithm problem in $G$ .
		ElGamal is malleable in an extreme way: for example, given an encryption $(c_1, c_2)$ of some (possibly unknown) message $m$ , one can easily construct an encryption $(c_1, 2 \cdot c_2)$ of the message $2m$ .
	psychcentral.com /psypsych/ElGamal (849 words)

	IEEE P1363: Asymmetric Encryption
		DHAES is built in a generic way from lower-level primitives: a symmetric encryption scheme, a message authentication code, group operations in an arbitrary group, and a cryptographic hash function.
		PSEC-2 is a public-key encryption system that uses the elliptic curve ElGamal trapdoor function, two random functions (hash functions) and a symmetric-key encryption (e.g., one-time padding and block-ciphers).
		PSEC-3 is a public-key encryption system that uses the elliptic curve El Gamal trapdoor function and two random functions (hash functions) as well as any semantically secure symmetric encryption scheme, such as the one-time pad, or any classical block-cipher.
	grouper.ieee.org /groups/1363/P1363a/Encryption.html (875 words)

	AusCERT - ESB-2003.0820 -- GnuPG Security Advisory -- GnuPG's ElGamal signing keys compromised
		Note that the standard keys as generated by GnuPG (DSA and ElGamal encryption) as well as RSA keys are NOT vulnerable.
		Note also that ElGamal signing keys cannot be generated without the use of a special flag to enable hidden options and even then overriding a warning message about this key type.
		Such a signature is always available for primary ElGamal keys because signatures created with that key are used to bind the user ID and other material to the primary key (self-signatures).
	www.auscert.org.au /render.html?it=3648 (1417 words)

	Identity-Based Encryption
		In 1984 Shamir asked for a public key encryption scheme in which the public key can be an arbitrary string.
		The performance of the cryptosystem is comparable to the performance of ElGamal encryption.
		The original motivation for identity-based encryption is to help the deployment of a public key infrastructure.
	crypto.stanford.edu /ibe (1483 words)

	Cryptography
		We use common primes for 2048 ElGamal encryption and decryption, and we currently only use ElGamal to encrypt the IV and session key in a single block, followed by the AES encrypted payload using that key and IV.
		The H(data) is the SHA256 of the data that is encrypted in the ElGamal block, and is preceeded by a random nonzero byte.
		ElGamal is never used on its own in I2P, but instead always as part of ElGamal/AES+SessionTag.
	www.i2p.net /how_cryptography (600 words)

	Articles - Asymmetric key algorithm (Site not responding. Last check: 2007-11-02)
		RSA uses exponentiation modulo a product of two large primes to encrypt and decrypt, performing both public key encryption and public key digital signature, and its security is connected to the presumed difficulty of factoring large integers, a problem for which there is no efficient (ie, practicably fast) general technique.
		The ElGamal cryptosystem (invented by Taher ElGamal then of Netscape) relies on the (similar, and related) difficulty of the discrete logarithm problem, as does the closely related DSA developed by the NSA and NIST.
		The most obvious application of a public key encryption system is confidentiality; a message which a sender encrypts using the recipient´s public key can only be decrypted by the recipient´s paired private key.
	www.centralairconditioners.net /articles/Asymmetric_key_algorithm (2963 words)

	The Secret Story of Nonsecret Encryption: Schneier (Site not responding. Last check: 2007-11-02)
		ElGamal encryption and ElGamal signatures are two quite different methods which are similar only in that they use Diffie-Hellman keys and are based on the difficulty of computing discrete logarithms.
		ElGamal encryption (which could also be called "Diffie-Hellman-Vernam" encryption because Diffie-Hellman is used to determine a Vernam key -- note that Vernam encryption works in any finite group, not just with XOR) _is_ in fact mentioned in one of the GCHQ papers.
		In M. Williamson: Thoughts on cheaper Non Secret Encryption (1976) , Williamson notes that x^{ab} can be used "as additive key to send a message".
	www.chiark.greenend.org.uk /pipermail/ukcrypto/1998-February/001181.html (245 words)

	Secure Chat Service Final Report John Porter CSC 8530 4
		The ElGamal encryption algorithm was used to implement this cipher.
		The ElGamal cipher is implemented in this project as a block cipher.
		The block sizes of the cipher depend on the size of its key, meaning that larger key sizes allow larger blocks of data to be encrypted at a time, data to be encrypted that does not completely fill a block will be padded to the correct length.
	www.csc.villanova.edu /~jporter/Final_Report.html (2160 words)

	[PGP-7340]: PGP Personal Privacy 6.0a, no key gen
		In order to foster interoperability and simplify encryption significantly for lots of folks who didn't want to know all the technical details but who wanted military-grade crypto (like me), Phil originally designed PGP as a "hybrid cryptosystem." This is a Very Good Thing.
		It means that PGP uses a specific set of algorithms to do the various jobs of symmetric encryption, asymmetric encryption and hashing: the set is commonly known as a "ciphersuite." It helps to understand the guts of a PGP message here a little.
		Anything over ~3072 bits is considered good, since asymmetric ElGamal encryption subkeys of approximately 3072 bits are roughly equivalent to symmetric CAST keys of 128 bits (the actual bit size varies from ~2900 to ~3100, but 3072 is in the pocket).
	www.chiark.greenend.org.uk /pipermail/ukcrypto/1998-October/002505.html (2114 words)

	MeMSoft - PGP FAQ (Site not responding. Last check: 2007-11-02)
		It has been proven that the ElGamal encryption scheme is equivalent to the DHP [MOV96], [TY98], [Sti95] - that is to say that if you can break either ElGamal or DH then you can also break the other (see Note 1).
		A conventional encryption algorithm is a function that maps an n-bit plaintext block to an n-bit ciphertext block where n is the blocksize.
		It is important in multiple encryption schemes that the underlying cipher is not a group; fortunately Campbell & Wiener have shown that DES is not a group [CW93].
	thunder.prohosting.com /mem/html/pgpfaq.html (13939 words)

	SecuriTeam™ - GnuPG's ElGamal Signing Keys Compromised
		Thus Werner has always dissuaded people from using ElGamal keys for signing; however they are still used and about 200 keys per year are generated and uploaded to the keyservers.
		All ElGamal sign+encrypt keys (type 20) generated with GnuPG 1.0.2 or later must be considered compromised.
		We have to distinguish between two cases: The primary key is ElGamal sign+encrypt versus just a subkey is ElGamal sign+encrypt.
	www.securiteam.com /securitynews/6F00V008UI.html (1055 words)

	PGP DH vs.RSA FAQ
		PGP actually implements ElGamal encryption [ElG85], which is a public-key encryption variant of the Diffie-Hellman Problem (DHP).
		Encryption is used to hide data - a compromise of the key would clearly make all messages readable and would thus make encryption entirely useless.
		Ble99] that there are no standards for implementing "pure" Elgamal signature schemes (in contrast to the DSS standard in respect of SDL signatures, for example) - and it is easy to fall in to one of the many pitfalls.
	www.samsimpson.com /cryptography/pgp/pgpfaqnew.html (14856 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		"On the security of ElGamal-based encryption" Abstract The ElGamal encryption scheme has been proposed several years ago and is one of the few probabilistic encryption schemes.
		In addition, we show that the opposite direction holds, i.e., the semantic security of the ElGamal encryption is actually equivalent to the decision Diffie-Hellman problem.
		Non-malleability is equivalent to the decision Diffie-Hellman assumption, the existence of a random oracle (in practice a secure hash function) or a trusted beacon (as needed for the Fiat-Shamir argument), and one assumption about the unforgeability of Schnorr signatures.
	www.ccs.neu.edu /home/yiannis/papers/egAbs.txt (166 words)

	Public-key cryptography (Site not responding. Last check: 2007-11-02)
		In particular, it must be impossible to decrypt using the public key, or to derive the private key from the public key.
		But the security of their system was eroded; circumstances were found in which parts of the encryption could be reversed, in a sequence of results spanning 10 years.
		Elgamal encryption invented by Egyptian cryptographer Taher Elgamal in 1984.
	www.cs.bham.ac.uk /~mdr/teaching/modules/security/lectures/public_key.html (2170 words)

	1. Background on public-key cryptography
		Diffie and Hellman's insight was to realize that there are cryptographic systems for which knowing the encryption key gives no help in decrypting messages.
		Our main tools for implementing encryption and decryption are computing primes and doing fast modular exponentiation as in section 1.2.6 of the textbook.
		The final element we need in order to implement ElGamal public-key encryption is a symmetric cipher, which will use the shared key to encrypt and decrypt.
	www-swiss.ai.mit.edu /classes/6.001/ST98/psets/ps2web/ps2-elgamal/node1.html (1758 words)

	[No title]
		All were coded in C++ or ported to C++ from C implementations, compiled with Microsoft Visual C++ 5.0 (optimize for speed, Pentium Pro code generation), and ran on a Pentium II 266MHz machine under Windows NT 4.0.
		ElGamal encryption and decryption use short exponents to save time.
		The size of the secret exponents were chosen so that a meet-in-the-middle attack would be slower than the general discrete log algorithm.
	www.ussrback.com /crypto/crypto_papers/algorithm_benchmarks.txt (482 words)

	Security Forums :: View topic - GnuPG's ElGamal signing keys compromised
		encryption) as well as RSA keys are NOT vulnerable.
		ElGamal signing keys cannot be generated without the use of a special
		We have to distinguish between two cases: The primary key is ElGamal
	www.security-forums.com /viewtopic.php?t=10329 (1135 words)

	Javascript cryptography page
		The ElGamal encryption was implemented using "Applied Cryptography" by B.Schneier (ISBN 0-471-11709-9) by G.Danezis.
		The ElGamal Signature Scheme was implemented by G.Danezis using as a reference the "Handbook of Applied cryptography" by Alfred J. Menezes, Paul C. van Oorschot and Scott A. Vanstone (ISBN 0-8493-8523-7)
		The parameters used for the ElGamal system are 768 bits long, and are the standard parameters used in the cryptix 3.2 cryptographic library.
	homes.esat.kuleuven.be /~gdanezis/ElGamal.html (288 words)

	RIM Device Java Library: Class ElGamalEncryptorEngine
		In ElGamal encryption, two parts are generated and both are required to decrypt data.
		The version of ElGamal that we implemented can be found in "Applied Cryptography", by Bruce Schneier, in section 19.6 (1996).
		Since the Certicom Cryptography API is already in the JDE, its use will remove the need for you to engage in time and resource intensive security integration so that you have lower development costs and a faster time to market.
	www.blackberry.com /developers/docs/4.1api/net/rim/device/api/crypto/ElGamalEncryptorEngine.html (1524 words)

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