Efficient algorithms for computing the Jacobi symbol
Journal of Symbolic Computation
Efficient private bidding and auctions with an oblivious third party
CCS '99 Proceedings of the 6th ACM conference on Computer and communications security
Password authenticated key exchange using hidden smooth subgroups
Proceedings of the 12th ACM conference on Computer and communications security
Computationally private information retrieval with polylogarithmic communication
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Single-database private information retrieval with constant communication rate
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Instantiability of RSA-OAEP under chosen-plaintext attack
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Improved cryptanalysis of the multi-prime φ-hiding assumption
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Optimal security proofs for full domain hash, revisited
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Reduction in lossiness of RSA trapdoor permutation
SPACE'12 Proceedings of the Second international conference on Security, Privacy, and Applied Cryptography Engineering
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Most cryptographic protocols, in particular asymmetricprotocols, are based on assumptions about the computationalcomplexity of mathematical problems. The Φ -Hidingassumption is such an assumption. It states that if p 1 and p 2 are small primes exactlyone of which divides φ (N ), where N is a number whose factorization is unknown and φ isEuler's totient function, then there is no polynomial-timealgorithm to distinguish which of the primes p 1 and p 2 dividesφ (N ) with a probability significantly greaterthan 1/2. In this paper, it will be shown that theΦ -Hiding assumption is not valid when applied to amodulus N = PQ 2e , whereP ,Q 2 are primes, e 0 is aninteger and P hides the prime in question. This indicatesthat cryptographic protocols using such moduli and relying on theΦ -Hiding assumption must be handled with care.