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Attacks on Shamir’s ‘RSA for paranoids’. (English) Zbl 1339.94044

Summary: In order to allow for efficient use of extremely large moduli, A. Shamir has proposed a variant of RSA in which one of the two prime factors is much smaller than the other [“RSA for paranoids”, CryptoBytes (The Technical Newsletter of RSA Laboratories) (1995), http://www.rsa.com/rsalabs/cryptobytes/]. This note points out that unless special precautions are taken, simple implementations of Shamir’s idea are subject to protocol attacks that recover the secret keys.

MSC:

94A60 Cryptography
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References:

[1] Hastad, J., On using RSA with low exponent in a public key network, (Williams, H. C., Advances in Cryptology—CRYPTO ’85. Advances in Cryptology—CRYPTO ’85, Lecture Notes in Computer Sci., Vol. 218 (1986), Springer: Springer Berlin), 403-408 · Zbl 0635.94008
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