A knapsack public-key cryptosystem based on elliptic curve discrete logarithm

Su, Pin-Chang; Lu, Erl-Huei; Chang, Henry Ker-Chang

doi:10.1016/j.amc.2004.08.027

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…Due to the performance advantages over other cryptosystems, the knapsack cryptosystems, as a typical class of PKCs, plays an important role in the wide variety of available cryptosystems. Especially, new knapsack-type cryptographic primitives have been developed in recent years, e.g., the non-injective knapsack cryptosystems [47], the knapsack Diffie-Hellman problem [48], and elliptic curve discrete logarithm based knapsack public-key cryptosystem [49].…”

Section: Discussionmentioning

confidence: 99%

PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density

et al. 2019

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By introducing an easy knapsack-type problem, a probabilistic knapsack-type public key cryptosystem (PKCHD) is proposed. It uses a Chinese remainder theorem to disguise the easy knapsack sequence. Thence, to recover the trapdoor information, the implicit attacker has to solve at least two hard number-theoretic problems, namely integer factorization and simultaneous Diophantine approximation problems. In PKCHD, the encryption function is nonlinear about the message vector. Under the re-linearization attack model, PKCHD obtains a high density and is secure against the low-density subset sum attacks, and the success probability for an attacker to recover the message vector with a single call to a lattice oracle is negligible. The infeasibilities of other attacks on the proposed PKCHD are also investigated. Meanwhile, it can use the hardest knapsack vector as the public key if its density evaluates the hardness of a knapsack instance. Furthermore, PKCHD only performs quadratic bit operations which confirms the efficiency of encrypting a message and deciphering a given cipher-text.

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Section: Discussionmentioning

confidence: 99%

PKCHD: Towards a Probabilistic Knapsack Public-Key Cryptosystem with High Density

et al. 2019

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“…-It is unclear whether the Koskinen scheme is secure against the simultaneous Diophantine approximation attack and the low-weight attack due to the lack of a technical analysis in the paper. -The security analysis of Su et al on their cryptosystem [29] is too simple. The security of the cryptosystem against the low-weight attacks, the simultaneous Diophantine approximation attacks, and the low-weight attacks needs to be carefully investigated.…”

Section: Remarkmentioning

confidence: 99%

“…Now, we compare our cryptosystem in Table 2 with other knapsack-type cryptosystems, mainly, the ChorRivest cryptosystem [3], the two cryptosystems proposed by Koskinen [8], and the scheme due to Su et al [29].…”

Section: Comparisonsmentioning

confidence: 99%