Precautions taken against various potential attacks

Abstract

This paper describes a “digital signature scheme giving message recovery” in order to submit it to the public scrutiny of IACR (the International Association for Cryptologic Research). This scheme is currently prepared by Subcommittee SC27, Security Techniques, inside Joint Technical Committee JTC1, Information Technology, established by both ISO (the International Organization for Standardization) and IEC (the International Electrotechnical Commission).

The digital signature scheme specified in DIS 9796 does not involve any hash-function. It allows a minimum resource requirement for verification. And it avoids various attacks against the generic algorithms in use.

Definition: An operation (addition, multiplication, power ...) modul n is “natural” when, being less than the modulus, the result does not involve the modulo reduction.

• Attacks by natural products — The exponential function is the basis of the signature schemes based upon RSA (odd verification exponents), and more generally, based upon exponentials in a ring (including even verification exponents). Under the exponential function, the image of a product of several constants is the product of the images of these constants. A subtle and efficient attack has been recently formulated by Don Coppersmith against annex D of CCITT X509, alias ISO/IEC 9594-8. The attacks by natural products have been definitely excluded in DIS 9796.

• Attacks by natural powers — If a natural v-th power is a legitimate argument of the secret function “raising to the power s mod n”, then anyone can easily produce the natural v-th root of this argument as a legitimate signature. And even more dangerous, if the verification exponent is even, then signing a natural v-th power may reveal the modulus factorization (cf. Rabin syndrom). In DIS 9796, the natural powers cannot be legitimate arguments to the secret function “raising to the power s mod n”.

DIS 9796 is under a 6-month DIS ballot (closed in september 1990) by ISO and IEC Members. This is a major step towards the adoption of an International Standard.

with the help of all the experts of ISO/IEC JTC1/SC27/WG20.2 and more specifically

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