RSA Moduli with a Predetermined Portion: Techniques and Applications

Abstract

Abstract. This paper discusses methods for generating RSA moduli with a predetermined portion. Predetermining a portion enables to represent RSA moduli in a compressed way, which gives rise to reduced transmission-and storage requirements. The first method described in this paper achieves the compression rate of known methods but is fully compatible with the fastest prime generation algorithms available on constrained devices. This is useful for devising a key escrow mechanism when RSA keys are generated on-board by tamper-resistant devices like smart cards. The second method in this paper is a compression technique yielding a compression rate of about 2/3 instead of 1/2. This results in higher savings in both transmission and storage of RSA moduli. In a typical application, a 2048-bit RSA modulus can fit on only 86 bytes (instead of 256 bytes for the regular representation). Of independent interest, the methods for prescribing bits in RSA moduli can be used to reduce the computational burden in a variety of cryptosystems.

Faster Interleaved Modular Multiplication Based on Barrett and Montgomery Reduction Methods

“…The methods describing how to generate such moduli in case of RSA are discussed in [16], [13]. Furthermore, from the sets proposed in this paper, one can also choose the primes that generate the RSA modulus to speed up a decryption of RSA by means of the Chinese Remainder Theorem (CRT).…”

“…Furthermore, Lenstra discusses security issues and concludes that the resulting moduli do not seem to offer less security than regular RSA moduli. In [13], Joye enhances the method for generating RSA moduli with a predetermined portion proposed in [16].…”

Upper bound of the length of information embedd in RSA public key efficiently

“…Joye proposed a method of revealing part of the private key to the administrator [3]. A user can show the administrator our secret key without revealing it to other persons by encrypting it with the symmetric key of the administrator and embedding it in the public key.…”

“…The administrator can manage the user's public key and secret key easily without needing to hold the secret key. In addition, Joye proposed a method of shortening the public key [3]. This method uses a small seed and a one-way hash function.…”

Speeding Up Bipartite Modular Multiplication

“…Furthermore, Lenstra discusses security issues and concludes that the resulting moduli do not seem to offer less security than regular RSA moduli. Joye [10] enhances the method for generating RSA moduli with a predetermined portion proposed in [12].…”