ABSTRACT We explore ideas for speeding up HFE-based signature schemes. In particular, we propose ... more ABSTRACT We explore ideas for speeding up HFE-based signature schemes. In particular, we propose an HFEv− system with odd characteristic and a secret map of degree 2. Changing the characteristic of the system has a profound effect, which we attempt to explain and also demonstrate through experiment. We discuss known attacks which could possibly topple such systems, especially algebraic attacks. After testing the resilience of these schemes against F4, we suggest parameters that yield acceptable security levels.
... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text... more ... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text | Download Full Text 0.70 MB PDF file. Degree PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences, 2009 . ...
This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modif... more This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modification of appending randomly chosen polynomials. Double-Layer Square uses a construction similar to some signature schemes, splitting the variables into two layers, one ...
This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic... more This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic arguments as well as experimental evidence to support the security claims. The first variant, Square-Vinegar with Embedding, uses a simple modification that nonetheless changes the nature of the public key polynomials. The second, 2-Square-Vinegar, is a more significant overhaul of the construction, using a bivariate secret map instead of a univariate one.
We use the signal function from the RLWE key exchange in [26] to derive an efficient zero knowled... more We use the signal function from the RLWE key exchange in [26] to derive an efficient zero knowledge authentication protocol to validate an RLWE key p = as + e with secret s and error e in the Random Oracle Model (ROM). With this protocol, a verifier can validate that a key p presented to him by a prover P is of the form p = as + e with s, e small and that the prover knows s. We accompany the description of the protocol with proof to show that it has negligible soundness and completeness error. The soundness of our protocol relies directly on the hardness of the RLWE problem. The protocol is applicable for both LWE and RLWE but we focus on the RLWE based protocol for efficiency and practicality. We also present a variant of the main protocol with a commitment scheme to avoid using the ROM.
Our department has experienced a significant culture transformation in its approach to teaching. ... more Our department has experienced a significant culture transformation in its approach to teaching. This change is primarily the result of sustained focus on reforming two heavily coordinated sequences, Applied Calculus and Calculus. Initially catalyzed by pilot projects introducing a flipped-class format to these courses, the reforms led to broader effects on the departmental culture. In this article, we describe the features of these reforms, and discuss how focusing on improving these coordinated courses led to departmental culture change. Finally, we share indicators of success and challenges faced.
... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text... more ... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text | Download Full Text 0.70 MB PDF file. Degree PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences, 2009 . ...
This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modif... more This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modification of appending randomly chosen polynomials. Double-Layer Square uses a construction similar to some signature schemes, splitting the variables into two layers, one ...
ABSTRACT We explore ideas for speeding up HFE-based signature schemes. In particular, we propose ... more ABSTRACT We explore ideas for speeding up HFE-based signature schemes. In particular, we propose an HFEv− system with odd characteristic and a secret map of degree 2. Changing the characteristic of the system has a profound effect, which we attempt to explain and also demonstrate through experiment. We discuss known attacks which could possibly topple such systems, especially algebraic attacks. After testing the resilience of these schemes against F4, we suggest parameters that yield acceptable security levels.
... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text... more ... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text | Download Full Text 0.70 MB PDF file. Degree PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences, 2009 . ...
This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modif... more This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modification of appending randomly chosen polynomials. Double-Layer Square uses a construction similar to some signature schemes, splitting the variables into two layers, one ...
This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic... more This paper proposes two ways to fix the broken Square-Vinegar signature scheme. We give heuristic arguments as well as experimental evidence to support the security claims. The first variant, Square-Vinegar with Embedding, uses a simple modification that nonetheless changes the nature of the public key polynomials. The second, 2-Square-Vinegar, is a more significant overhaul of the construction, using a bivariate secret map instead of a univariate one.
We use the signal function from the RLWE key exchange in [26] to derive an efficient zero knowled... more We use the signal function from the RLWE key exchange in [26] to derive an efficient zero knowledge authentication protocol to validate an RLWE key p = as + e with secret s and error e in the Random Oracle Model (ROM). With this protocol, a verifier can validate that a key p presented to him by a prover P is of the form p = as + e with s, e small and that the prover knows s. We accompany the description of the protocol with proof to show that it has negligible soundness and completeness error. The soundness of our protocol relies directly on the hardness of the RLWE problem. The protocol is applicable for both LWE and RLWE but we focus on the RLWE based protocol for efficiency and practicality. We also present a variant of the main protocol with a commitment scheme to avoid using the ROM.
Our department has experienced a significant culture transformation in its approach to teaching. ... more Our department has experienced a significant culture transformation in its approach to teaching. This change is primarily the result of sustained focus on reforming two heavily coordinated sequences, Applied Calculus and Calculus. Initially catalyzed by pilot projects introducing a flipped-class format to these courses, the reforms led to broader effects on the departmental culture. In this article, we describe the features of these reforms, and discuss how focusing on improving these coordinated courses led to departmental culture change. Finally, we share indicators of success and challenges faced.
... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text... more ... Square: A New Family of Multivariate Encryption Schemes. Clough, Crystal L. Display Full Text | Download Full Text 0.70 MB PDF file. Degree PhD, University of Cincinnati, Arts and Sciences : Mathematical Sciences, 2009 . ...
This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modif... more This paper discusses two encryption schemes to fix the Square scheme. Square+ uses the Plus modification of appending randomly chosen polynomials. Double-Layer Square uses a construction similar to some signature schemes, splitting the variables into two layers, one ...
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