Practical Attacks Against the Walnut Digital Signature Scheme

Recently, NIST started the process of standardizing quantum- resistant public-key cryptographic algorithms. WalnutDSA, the subject of this paper, is one of the 20 proposed signature schemes that are being considered for standardization. Walnut relies on a one-way function called E-Multiplication, which has a rich algebraic structure. This paper shows that this structure can be exploited to launch several practical attacks against the Walnut cryptosystem. The attacks work very well in practice; it is possible to forge signatures and compute equivalent secret keys for the 128-bit and 256-bit security parameters submitted to NIST in less than a second and in less than a minute respectively

On the Security of Diffie-Hellman Bits

Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a "hidden" element α of a finite field IFp of p elements from rather short strings of the most significant bits of the remainder modulo p o