Abstract
Most cryptographic protocols, in particular asymmetric protocols, are based on assumptions about the computational complexity of mathematical problems. The Φ-Hiding assumption is such an assumption. It states that if p 1 and p 2 are small primes exactly one of which divides ϕ(N), where N is a number whose factorization is unknown and ϕ is Euler’s totient function, then there is no polynomial-time algorithm to distinguish which of the primes p 1 and p 2 divides ϕ(N) with a probability significantly greater than 1/2. In this paper, it will be shown that the Φ-Hiding assumption is not valid when applied to a modulus N = PQ 2e, where P,Q > 2 are primes, e > 0 is an integer and P hides the prime in question. This indicates that cryptographic protocols using such moduli and relying on the Φ-Hiding assumption must be handled with care.
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Schridde, C., Freisleben, B. (2008). On the Validity of the Φ-Hiding Assumption in Cryptographic Protocols. In: Pieprzyk, J. (eds) Advances in Cryptology - ASIACRYPT 2008. ASIACRYPT 2008. Lecture Notes in Computer Science, vol 5350. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89255-7_21
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DOI: https://doi.org/10.1007/978-3-540-89255-7_21
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