Torsion point attacks on ‘SIDH‐like’ cryptosystems

Attacks to polynomial cryptosystems

In this paper we review some possible attacks to cryptosystems based on the problem of multivariate quadratic equations (MQ). After introducing the MQ problem and sketching schemes to generate private and public keys for these cryptosystems, we present well-known attacks based attacks based on the Gröbner bases computation to solve multivariate systems. The MQ problem The MQ problem consists in...

Differential Fault Attacks on Elliptic Curve Cryptosystems

In this paper we extend the ideas for differential fault attacks on the RSA cryptosystem (see [4]) to schemes using elliptic curves. We present three different types of attacks that can be used to derive information about the secret key if bit errors can be inserted into the elliptic curve computations in a tamper-proof device. The effectiveness of the attacks was proven in a software simulatio...

Faster Attacks on Elliptic Curve Cryptosystems

The previously best attack known on elliptic curve cryptosystems used in practice was the parallel collision search based on Pollard's-method. The complexity of this attack is the square root of the prime order of the generating point used. For arbitrary curves, typically deened over GF(p) or GF(2 m), the attack time can be reduced by a factor or p 2, a small improvement. For subbeld curves, th...

Further Attacks on Server-aided Rsa Cryptosystems

Lim and Lee 5] describe protocols for server-aided RSA digital signatures involving moduli N with special structure: N = pq where p and q are both of order N 1=2 , and p ? 1 and q ? 1 have a large common factor. We describe a method to factor such numbers in time O ? N 1=4 == and show that this renders the proposed system insecure.

Fault Attacks on Elliptic Curve Cryptosystems