An efficient and secure RSA--like cryptosystem exploiting R\'edei rational functions over conics

We define an isomorphism between the group of points of a conic and the set of integers modulo a prime equipped with a non-standard product. This product can be efficiently evaluated through the use of R\'edei rational functions. We then exploit the isomorphism to construct a novel RSA-like scheme. We compare our scheme with classic RSA and with RSA-like schemes based on the cubic or conic equation. The decryption operation of the proposed scheme turns to be two times faster than RSA, and involves the lowest number of modular inversions with respect to other RSA-like schemes based on curves. Our solution offers the same security as RSA in a one-to-one communication and more security in broadcast applications.Comment: 18 pages, 1 figur

The Myth of Superiority of American Encryption Products

Encryption software and hardware use sophisticated mathematical algorithms to encipher a message so that only the intended recipient may read it. Fearing that criminals and terrorists will use encryption to evade authorities, the United States now restricts the export of encryption products with key lengths of more than 56 bits. The controls are futile, because strong encryption products are readily available overseas. Foreign-made encryption products are as good as, or better than, U.S.-made products. U.S. cryptographers have no monopoly on the mathematical knowledge and methods used to create strong encryption. Powerful encryption symmetric-key technologies developed in other countries include IDEA and GOST. Researchers in New Zealand have developed very strong public-key encryption systems. As patents on strong algorithms of U.S. origin expire, researchers in other countries will gain additional opportunities to develop strong encryption technology based on those algorithms

Asymmetric Leakage from Multiplier and Collision-Based Single-Shot Side-Channel Attack

The single-shot collision attack on RSA proposed by Hanley et al. is studied focusing on the difference between two operands of multiplier. It is shown that how leakage from integer multiplier and long-integer multiplication algorithm can be asymmetric between two operands. The asymmetric leakage is verified with experiments on FPGA and micro-controller platforms. Moreover, we show an experimental result in which success and failure of the attack is determined by the order of operands. Therefore, designing operand order can be a cost-effective countermeasure. Meanwhile we also show a case in which a particular countermeasure becomes ineffective when the asymmetric leakage is considered. In addition to the above main contribution, an extension of the attack by Hanley et al. using the signal-processing technique of Big Mac Attack is presented