A Further Weakness in the Common Modulus Protocol for the Rsa Cryptoalgorithm

Breaking RSA May Be As Difficult As Factoring

“…A private exponent can be used to build a straight line program for solving the RSA problem. Conversely, however, it is not clear that a straight line program for solving the RSA problem reveals a private exponent, so the result in this paper is not immediate from [dL84,Mil76].…”

“…Obfuscation seems to be the main new hurdle that this result overcomes. Furthermore, unlike known results [dL84,Mil76], this result is limited to public exponents with small factors.…”

“…Some of the best surveys [Bon99,RK] of the RSA problem, however, do not mention such a result. Although arguably not of major importance, in that [dL84,Mil76] covers most of this ground, the result seems important enough to be made more widely known. Anybody who has already published, or even previously discovered and communicated, this result may be duly credited in an update of this paper.…”

“…With a smallest factor of two, the well known reductions [dL84,Mil76] are very tight and are not limited to straight line programs. With a smallest factor of three, the reduction described here is quite tight, but limited to straight line programs.…”

“…Chances are that such a straight line program would reveal the decryption exponent, unless it were very well obfuscated. If the decryption exponent were revealed by the straight line program, then known results [dL84,Mil76] reveal the factorization, so the result accomplishes nothing new. Obfuscation seems to be the main new hurdle that this result overcomes.…”