In this paper, we lower the upper bound of the number of solutions of oracletransformation polynomial F(x) over GF(q) So one can also recover all the secrete keys with fewercalls We use our generalized ' even-and-...In this paper, we lower the upper bound of the number of solutions of oracletransformation polynomial F(x) over GF(q) So one can also recover all the secrete keys with fewercalls We use our generalized ' even-and-odd test' method to recover the least significant p-adic'bits' of representations of the Lucas Cryptosystem secret keys x Finally, we analyze the EfficientCompact Subgroup Trace Representation (XTR) Diffic-Hellmen secrete keys and point out that if theorder of XIR-subgroup has a specialform then all the bits of the secrete key of XIR ean be recoveredform any bit of the exponent x.展开更多
文摘In this paper, we lower the upper bound of the number of solutions of oracletransformation polynomial F(x) over GF(q) So one can also recover all the secrete keys with fewercalls We use our generalized ' even-and-odd test' method to recover the least significant p-adic'bits' of representations of the Lucas Cryptosystem secret keys x Finally, we analyze the EfficientCompact Subgroup Trace Representation (XTR) Diffic-Hellmen secrete keys and point out that if theorder of XIR-subgroup has a specialform then all the bits of the secrete key of XIR ean be recoveredform any bit of the exponent x.
