How to construct random functions
Journal of the ACM (JACM)
How to construct pseudorandom permutations from pseudorandom functions
SIAM Journal on Computing - Special issue on cryptography
Impossibility and optimally results on constructing pseudorandom permutations (extended abstract)
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the security of Schnorr's pseudo random generator
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Differential cryptanalysis of the data encryption standard
Differential cryptanalysis of the data encryption standard
On the construction of pseudo-random permutations: Luby-Rackoff revisited (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved security bounds for pseudorandom permutations
Proceedings of the 4th ACM conference on Computer and communications security
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
SQUARE HASH: Fast Message Authenication via Optimized Universal Hash Functions
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
New Results on Pseudorandom Permutation Generators Based on the DES Scheme
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
The Security of Cipher Block Chaining
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Towards Making Luby-Rackoff Ciphers Optimal and Practical
FSE '99 Proceedings of the 6th International Workshop on Fast Software Encryption
On the universal hash functions in Luby-Rackoff cipher
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Efficient constructions of variable-input-length block ciphers
SAC'04 Proceedings of the 11th international conference on Selected Areas in Cryptography
Tweakable enciphering schemes using only the encryption function of a block cipher
Information Processing Letters
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This work initiates a study of Luby-Rackoff ciphers when the bitwise exclusive-or (XOR) operation in the underlying Feistel network is replaced by a binary operation in an arbitrary finite group. We obtain various interesting results in this context: -First, we analyze the security of three-round Feistel ladders over arbitrary groups. We examine various Luby-Rackoff ciphers known to be insecure when XOR is used. In some cases, we can break these ciphers over arbitrary Abelian groups and in other cases, however, the security remains an open problem. -Next, we construct a four round Luby-Rackoff cipher, operating over finite groups of characteristic greater than 2, that is not only completely secure against adaptive chosen plaintext and ciphertext attacks, but has better time / space complexity and uses fewer random bits than all previously considered Luby-Rackoff ciphers of equivalent security in the literature. Surprisingly, when the group is of characteristic 2 (i.e., the underlying operation on strings is bitwise exclusive-or), the cipher can be completely broken in a constant number of queries.Notably, for the former set of results dealing with three rounds (where we report no difference) we need new techniques. However for the latter set of results dealing with four rounds (where we prove a new theorem) we rely on a generalization of known techniques albeit requires a new type of hash function family, called a monosymmetric hash function family, which we introduce in this work. We also discuss the existence (and construction) of this function family over various groups, and argue the necessity of this family in our construction. Moreover, these functions can be very easily and efficiently implemented on most current microprocessors thereby rendering the four round construction very practical.