A Digital Signature Scheme Based on MST₃ Cryptosystems

Table 2

Number of basic operations for public key generation.

	Secret key 𝛽	Secret key [𝑡0,…,𝑡𝑠]	Public key 𝛼	Public key 𝛾
𝔽2^𝑚 ADD	𝑇^3	—	𝑇	9𝑇+𝑠
𝔽2^𝑚 MULT	—	𝑠+1^4	𝑇−𝑠	2𝑇+𝑠
𝔽2^𝑚 PRNG	∑^𝑣𝑙=1𝑟^∗𝑙^5	2(𝑠+1)	2𝑇−𝑠	—

³𝑇=∑^𝑠_𝑖=1𝑟_𝑖, 𝑟_𝑖=∏^𝑢𝑖_𝑗=1𝑟^∗_𝑖𝑗⋅𝑤_𝑖 for 1≤𝑖≤𝑠 and ∑^𝑠_𝑖=1𝑢_𝑖=𝑣, where 𝑤_𝑖=0if𝑢_𝑖=11if𝑢_𝑖>1.
4For 𝑎∈𝔽_𝑞, 𝜃∶𝑎→𝑎² is a Frobenius automorphism. Hence, 𝜃 can be reduced to a multiplication.
⁵𝑣 represents the number of blocks before fusion.