Abstract
RSA (Rivest, Shamir and Adleman) is today’s most popular public key encryption scheme. Batch-RSA (due to Fiat) is a method to compute many (n/log 22 (n), where n is the security parameter) RSA decryption operations at a computational cost approaching that of one normal decryption. It requires that all the operations use the same modulus, but distinct, relatively prime in pairs, short, public exponents. A star-like key agreement scheme could use such a system to slash computational complexity at the center. We show a real life example of such a system — secure portable telephony. Unfortunately, in this system Batch-RSA cannot be employed effectively, due to a delay component which arises from the nature of RSA key exchange. We show that mathematical ideas similar to Fiat’s can lead to a Batch-Diffie-Hellman key agreement scheme, that does not suffer such delay and is comparable in efficiency to Batch-RSA. We prove that with some precautions, this system is as hard to break as RSA with short public exponent. In practice our method improves processing time at the center by a factor of 6 to 17 when compared to (non-batch) Diffie-Hellman schemes with full-size exponents and moduli in the practical range. Smaller improvements (on the order of 1.6 to 3) are obtainable when compared to a Diffie-Hellman scheme employing abbreviated exponents.
June 19, 1991
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© 1993 Springer-Verlag Berlin Heidelberg
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Beller, M.J., Yacobi, Y. (1993). Batch Diffie-Hellman Key Agreement Systems and their Application to Portable Communications. In: Rueppel, R.A. (eds) Advances in Cryptology — EUROCRYPT’ 92. EUROCRYPT 1992. Lecture Notes in Computer Science, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47555-9_19
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